Boosting Win Probability accuracy with player embeddings

In my previous post Computing Win Probability of T20 matches I had discussed various approaches on computing Win Probability of T20 matches. I had created ML models with glmnet and random forest using TidyModels. This was what I had achieved

  • glmnet : accuracy – 0.67 and sensitivity/specificity – 0.68/0.65
  • random forest : accuracy – 0.737 and roc_auc- 0.834
  • DL model with Keras in Python : accuracy – 0.73

I wanted to see if the performance of the models could be further improved. I got a suggestion from a AI/DL whizkid, who is close to me, to include embeddings for batsmen and bowlers. He felt that win percentage is influenced by which batsman faces which bowler.

So, I started to explore this idea. Embeddings can be used to convert categorical variables to a vector of continuous floating point numbers.Fortunately R’s Tidymodels, has a convenient functionality to create embeddings. By including embeddings for batsman, bowler the performance of my ML models improved vastly. Now the performance is

  • glmnet : accuracy – 0.728 and roc_auc – 0.81
  • random forest : accuracy – 0.927 and roc_auc – 0.98
  • mlp-dnn :accuracy – 0.762 and roc_auc – 0.854

As can be seem there is almost a 20% increase in accuracy with random forests with embeddings over the model without embeddings. Moreover, the feature importance which is plotted below shows that the bowler and batsman embeddings have a significant influence on the Win Probability

Note: The data for this analysis is taken from Cricsheet and has been processed with my R package yorkr.

A. Win Probability using GLM with penalty and player embeddings

Here Generalised Linear Model (GLMNET) for Logistic Regression is used. In the GLMNET the regularisation path is computed for the lasso or elastic net penalty at a grid of values for the regularisation parameter lambda. glmnet is extremely fast and gave an accuracy of 0.72 for an roc_auc of 0.81 with batsman, bowler embeddings. This was good improvement over my earlier implementation with glmnet without the batsman & bowler embeddings which had a

  1. Read the data

a) Read the data from 9 T20 leagues (BBL, CPL, IPL, NTB, PSL, SSM, T20 Men, T20 Women, WBB) and create a single data frame of ball-by-ball data. Display the data frame

library(dplyr)
library(caret)
library(e1071)
library(ggplot2)
library(tidymodels)  
library(embed)

# Helper packages
library(readr)       # for importing data
library(vip) 

df1=read.csv("output3/matchesBBL3.csv")
df2=read.csv("output3/matchesCPL3.csv")
df3=read.csv("output3/matchesIPL3.csv")
df4=read.csv("output3/matchesNTB3.csv")
df5=read.csv("output3/matchesPSL3.csv")
df6=read.csv("output3/matchesSSM3.csv")
df7=read.csv("output3/matchesT20M3.csv")
df8=read.csv("output3/matchesT20W3.csv")
df9=read.csv("output3/matchesWBB3.csv")

#Bind all dataframes together
df=rbind(df1,df2,df3,df4,df5,df6,df7,df8,df9)
glimpse(df)
Rows: 1,199,115
Columns: 10
$ batsman        <chr> "JD Smith", "M Klinger", "M Klinger", "M Klinger", "JD …
$ bowler         <chr> "NM Hauritz", "NM Hauritz", "NM Hauritz", "NM Hauritz",…

$ ballNum        <int> 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, …
$ ballsRemaining <int> 125, 124, 123, 122, 121, 120, 119, 118, 117, 116, 115, …
$ runs           <int> 1, 1, 2, 3, 3, 3, 4, 4, 5, 5, 6, 7, 13, 14, 16, 18, 18,…

$ runRate        <dbl> 1.0000000, 0.5000000, 0.6666667, 0.7500000, 0.6000000, …
$ numWickets     <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1…
$ runsMomentum   <dbl> 0.08800000, 0.08870968, 0.08943089, 0.09016393, 0.09090…
$ perfIndex      <dbl> 11.000000, 5.500000, 7.333333, 8.250000, 6.600000, 5.50…
$ isWinner       <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…


df %>% 
  count(isWinner) %>% 
  mutate(prop = n/sum(n))
  isWinner      n      prop
1        
0 614237 0.5122419
2        
1 584878 0.4877581

2) Create training.validation and test sets

b) Split to training, validation and test sets. The dataset is initially split into training and test in the ratio 80%:20%. The training data is again split into training and validation in the ratio 80:20

set.seed(123)
splits      <- initial_split(df,prop = 0.80)
splits
<Training/Testing/Total>
<959292/239823/1199115>
df_other <- training(splits)
df_test  <- testing(splits)

set.seed(234)
val_set <- validation_split(df_other,prop = 0.80)
val_set
# A tibble: 1 × 2
  splits                  
id        
  <list>                  <chr>     
1 <split [767433/191859]> validation

3) Create pre-processing recipe

a) Normalise the following predictors

  • ballNum
  • ballsRemaining
  • runs
  • runRate
  • numWickets
  • runsMomentum
  • perfIndex

b) Create floating point embeddings for

  • batsman
  • bowler

4) Create a Logistic Regression Workflow by adding the GLM model and the recipe

5) Create grid of elastic penalty values for regularisation

6) Train all 30 models

7) Plot the ROC of the model against the penalty

# Use all 12 cores
cores <- parallel::detectCores()
cores
# Create a Logistic Regression model with penalty
lr_mod <- 
  logistic_reg(penalty = tune(), mixture = 1) %>% 
  set_engine("glmnet",num.threads = cores)

# Create pre-processing recipe
lr_recipe <- 
  recipe(isWinner ~ ., data = df_other) %>%
  step_embed(batsman,bowler, outcome = vars(isWinner)) %>%  step_normalize(ballNum,ballsRemaining,runs,runRate,numWickets,runsMomentum,perfIndex) 

# Set the workflow by adding the GLM model with the recipe
lr_workflow <- 
  workflow() %>% 
  add_model(lr_mod) %>% 
  add_recipe(lr_recipe)

# Create a grid for the elastic net penalty
lr_reg_grid <- tibble(penalty = 10^seq(-4, -1, length.out = 30))
lr_reg_grid %>% top_n(-5) 
# A tibble: 5 × 1
   penalty
     
<dbl>
1 0.0001  
2 0.000127
3 0.000161
4 0.000204
5 0.000259

lr_reg_grid %>% top_n(5)  # highest penalty values
# A tibble: 5 × 1
  penalty
    <dbl>
1  0.0386
2  0.0489
3  0.0621
4  0.0788
5  0.1

# Train 30 penalized models
lr_res <- 
  lr_workflow %>% 
  tune_grid(val_set,
            grid = lr_reg_grid,
            control = control_grid(save_pred = TRUE),
            metrics = metric_set(accuracy,roc_auc))

# Plot the penalty versus ROC
lr_plot <- 
  lr_res %>% 
  collect_metrics() %>% 
  ggplot(aes(x = penalty, y = mean)) + 
  geom_point() + 
  geom_line() + 
  ylab("Area under the ROC Curve") +
  scale_x_log10(labels = scales::label_number())

lr_plot

The Penalty vs ROC plot is shown below

8) Display the ROC_AUC of the top models with the penalty

9) Select the model with the best ROC_AUC and the associated penalty. It can be seen the best mean ROC_AUC is 0.81 and the associated penalty is 0.000530

top_models <-
  lr_res %>% 
  show_best("roc_auc", n = 15) %>% 
  arrange(penalty) 
top_models

# A tibble: 15 × 7
    penalty .metric .estimator  mean     n std_err .config              
      <dbl> <chr>   <chr>      <dbl> <int>   <dbl> <chr>                
 1 0.0001   roc_auc binary     0.810     1      NA Preprocessor1_Model01
 2 0.000127 roc_auc binary     0.810     1      NA Preprocessor1_Model02
 3 0.000161 roc_auc binary     0.810     1      NA Preprocessor1_Model03
 4 0.000204 roc_auc binary     0.810     1      NA Preprocessor1_Model04
 5 0.000259 roc_auc binary     0.810     1      NA Preprocessor1_Model05
 6 0.000329 roc_auc binary     0.810     1      NA Preprocessor1_Model06
 7 0.000418 roc_auc binary     0.810     1      NA Preprocessor1_Model07
 8 0.000530 roc_auc binary     0.810     1      NA Preprocessor1_Model08
 9 0.000672 roc_auc binary     0.810     1      NA Preprocessor1_Model09
10 0.000853 roc_auc binary     0.810     1      NA Preprocessor1_Model10
11 0.00108  roc_auc binary     0.810     1      NA Preprocessor1_Model11
12 0.00137  roc_auc binary     0.810     1      NA Preprocessor1_Model12
13 0.00174  roc_auc binary     0.809     1      NA Preprocessor1_Model13
14 0.00221  roc_auc binary     0.809     1      NA Preprocessor1_Model14
15 0.00281  roc_auc binary     0.809     1      NA Preprocessor1_Model15

#Picking the best model and the corresponding penalty
lr_best <- 
  lr_res %>% 
  collect_metrics() %>% 
  arrange(penalty) %>% 
  slice(8)
lr_best
# A tibble: 1 × 7
   
   penalty .metric .estimator  mean     n std_err .config              
     <dbl> <chr>   <chr>      <dbl> <int>   <dbl> <chr>                

1 0.000530 roc_auc binary     0.810     1      NA Preprocessor1_Model08

# Collect predictions and generate the AUC curve
lr_auc <- 
  lr_res %>% 
  collect_predictions(parameters = lr_best) %>% 
  roc_curve(isWinner, .pred_0) %>% 
  mutate(model = "Logistic Regression")

autoplot(lr_auc)

7) Plot the Area under the Curve (AUC).

10) Build the final model with the best LR parameters value as found in lr_best

a) The best performance was for a penalty of 0.000530

b) The accuracy achieved is 0.72. Clearly using the embeddings for batsman, bowlers improves on the performance of the GLM model without the embeddings. The accuracy achieved was 0.72 whereas previously it was 0.67 see (Computing Win Probability of T20 Matches)

c) Create a fit with the best parameters

d) The accuracy is 72.8% and the ROC_AUC is 0.813

# Create a model with the penalty for best ROC_AUC
last_lr_mod <- 
  logistic_reg(penalty = 0.000530, mixture = 1) %>% 
  set_engine("glmnet",num.threads = cores,importance = "impurity")

#Update the workflow with this model
last_lr_workflow <- 
  lr_workflow %>% 
  update_model(last_lr_mod)

#Create a fit
set.seed(345)
last_lr_fit <- 
  last_lr_workflow %>% 
  last_fit(splits)

#Generate accuracy, roc_auc
last_lr_fit %>% 
  collect_metrics()
# A tibble: 2 × 4
  .metric  .estimator .estimate .config             
  
<chr>    <chr>          <dbl> <chr>               
1 accuracy binary         0.728 Preprocessor1_Model1

2 roc_auc  binary         0.813 Preprocessor1_Model1

11) Plot the feature importance

It can be seen that bowler and batsman embeddings are the most significant for the prediction followed by runRate.

runRate –

  • runRate in 1st innings
  • requiredRunRate in 2nd innings

12) Plot the ROC characteristics

last_lr_fit %>% 
  collect_predictions() %>% 
  roc_curve(isWinner, .pred_0) %>% 
  autoplot()

13) Generate a confusion matrix

14) Create a final Generalised Linear Model for Logistic Regression with the penalty of 0.000530

15) Save the model

# generate predictions from the test set
test_predictions <- last_lr_fit %>% collect_predictions()
test_predictions

# generate a confusion matrix
test_predictions %>% 
  conf_mat(truth = isWinner, estimate = .pred_class)

Truth
Prediction     0     1
         
0                  90105 32658
         
1                  32572 84488

final_lr_model <- fit(last_lr_workflow, df_other)

final_lr_model

obj_size(final_lr_model)
146.51 MB


butcher::weigh(final_lr_model)
A tibble: 305 × 2
object                                  size
<chr>                                  <dbl>
  1 pre.actions.recipe.recipe.steps.terms1  57.9
2 pre.actions.recipe.recipe.steps.terms2  57.9
3 pre.actions.recipe.recipe.steps.terms3  57.9


cleaned_lm <- butcher::axe_env(final_lr_model, verbose = TRUE)
#✔ Memory released: "1.04 kB"
#✔ Memory released: "1.62 kB"

saveRDS(cleaned_lm, "cleanedLR.rds")
  

16) Compute Ball-by-ball Win Probability

  • Chennai Super Kings-Lucknow Super Giants-2022-03-31

16a) The corresponding Worm-wicket graph for this match is as below

  • Chennai Super Kings-Lucknow Super Giants-2022-03-31

B) Win Probability using Random Forest with player embeddings

In the 2nd approach I use Random Forest with batsman and bowler embeddings. The performance of the model with embeddings is quantum jump from the earlier performance without embeddings. However, the random forest is also computationally intensive.

1) Read the data

a) Read the data from 9 T20 leagues (BBL, CPL, IPL, NTB, PSL, SSM, T20 Men, T20 Women, WBB) and create a single data frame of ball-by-ball data. Display the data frame

2) Create training.validation and test sets

b) Split to training, validation and test sets. The dataset is initially split into training and test in the ratio 80%:20%. The training data is again split into training and validation in the ratio 80:20

library(dplyr)
library(caret)
library(e1071)
library(ggplot2)
library(tidymodels)  
library(tidymodels)  
library(embed)

# Helper packages
library(readr)       # for importing data
library(vip) 
library(ranger)

# Read all the 9 T20 leagues
df1=read.csv("output3/matchesBBL3.csv")
df2=read.csv("output3/matchesCPL3.csv")
df3=read.csv("output3/matchesIPL3.csv")
df4=read.csv("output3/matchesNTB3.csv")
df5=read.csv("output3/matchesPSL3.csv")
df6=read.csv("output3/matchesSSM3.csv")
df7=read.csv("output3/matchesT20M3.csv")
df8=read.csv("output3/matchesT20W3.csv")
df9=read.csv("output3/matchesWBB3.csv")

# Bind into a single dataframe
df=rbind(df1,df2,df3,df4,df5,df6,df7,df8,df9)

set.seed(123)
df$isWinner = as.factor(df$isWinner)

#Split data into training, validation and test sets
splits      <- initial_split(df,prop = 0.80)
df_other <- training(splits)
df_test  <- testing(splits)
set.seed(234)
val_set <- validation_split(df_other, prop = 0.80)
val_set

2) Create a Random Forest model tuning for number of predictor nodes at each decision node (mtry) and minimum number of predictor nodes (min_n)

3) Use the ranger engine and set up for classification

4) Set up the recipe and include batsman and bowler embeddings

5) Create a workflow and add the recipe and the random forest model with the tuning parameters

# Use all 12 cores parallely
cores <- parallel::detectCores()
cores
[1] 12

# Create the random forest model with mtry and min as tuning parameters
rf_mod <- 
  rand_forest(mtry = tune(), min_n = tune(), trees = 1000) %>% 
  set_engine("ranger", num.threads = cores) %>% 
  set_mode("classification")

# Setup the recipe with batsman and bowler embeddings
rf_recipe <- 
  recipe(isWinner ~ ., data = df_other) %>% 
  step_embed(batsman,bowler, outcome = vars(isWinner)) 

# Create the random forest workflow
rf_workflow <- 
  workflow() %>% 
  add_model(rf_mod) %>% 
  add_recipe(rf_recipe)

rf_mod
# show what will be tuned
extract_parameter_set_dials(rf_mod)

set.seed(345)
# specify which values meant to tune

# Build the model
rf_res <- 
  rf_workflow %>% 
  tune_grid(val_set,
            grid = 10,
            control = control_grid(save_pred = TRUE),
            metrics = metric_set(accuracy,roc_auc))

# Pick the best  roc_auc and the associated tuning parameters
rf_res %>% 
  show_best(metric = "roc_auc")
# A tibble: 5 × 8
   mtry min_n .metric .estimator  mean     n std_err .config              
  <int> <int> <chr>   <chr>      <dbl> <int>   <dbl> <chr>                
1     4     4 roc_auc binary     0.980     1      NA Preprocessor1_Model08
2     9     8 roc_auc binary     0.979     1      NA Preprocessor1_Model03

3     8    16 roc_auc binary     0.974     1      NA Preprocessor1_Model10
4     7    22 roc_auc binary     0.969     1      NA Preprocessor1_Model09

5     5    19 roc_auc binary     0.969     1      NA Preprocessor1_Model06

rf_res %>% 
  show_best(metric = "accuracy")
# A tibble: 5 × 8
   
mtry min_n .metric  .estimator  mean     n std_err .config              
  <int> <int> <chr>    <chr>      <dbl> <int>   <dbl> <chr>                
1  4     4 accuracy binary    0.927     1      NA Preprocessor1_Model08

2  9     8 accuracy binary    0.926     1      NA Preprocessor1_Model03
3  8    16 accuracy binary    0.915     1      NA Preprocessor1_Model10
4  7    22 accuracy binary    0.906     1      NA Preprocessor1_Model09

5  5    19 accuracy binary    0.904     1      NA Preprocessor1_Model0

6) Select all models with the best roc_auc. It can be seen that the best roc_auc is 0.980 for mtry=4 and min_n=4

7) Get the model with the highest accuracy. The highest accuracy achieved is 0.927 or 92.7. This accuracy is also for mtry=4 and min_n=4

# Pick the best  roc_auc and the associated tuning parameters
rf_res %>% 
  show_best(metric = "roc_auc")
# A tibble: 5 × 8
   mtry min_n .metric .estimator  mean     n std_err .config              
  <int> <int> <chr>   <chr>      <dbl> <int>   <dbl> <chr>                
1     4     4 roc_auc binary     0.980     1      NA Preprocessor1_Model08
2     9     8 roc_auc binary     0.979     1      NA Preprocessor1_Model03

3     8    16 roc_auc binary     0.974     1      NA Preprocessor1_Model10
4     7    22 roc_auc binary     0.969     1      NA Preprocessor1_Model09

5     5    19 roc_auc binary     0.969     1      NA Preprocessor1_Model06

# Display the accuracy of the models in descending order and the parameters
rf_res %>% 
  show_best(metric = "accuracy")
# A tibble: 5 × 8
   
mtry min_n .metric  .estimator  mean     n std_err .config              
  <int> <int> <chr>    <chr>      <dbl> <int>   <dbl> <chr>                
1  4     4 accuracy binary    0.927     1      NA Preprocessor1_Model08

2  9     8 accuracy binary    0.926     1      NA Preprocessor1_Model03
3  8    16 accuracy binary    0.915     1      NA Preprocessor1_Model10
4  7    22 accuracy binary    0.906     1      NA Preprocessor1_Model09

5  5    19 accuracy binary    0.904     1      NA Preprocessor1_Model0

8) Select the model with the best parameters for accuracy mtry=4 and min_n=4. For this the accuracy is 0.927. For this configuration the roc_auc is also the best at 0.980

9) Plot the Area Under the Curve (AUC). It can be seen that this model performs really well and it hugs the top left.

# Pick the best model
rf_best <- 
  rf_res %>% 
  select_best(metric = "accuracy")

# The best model has mtry=4 and min=4
rf_best
     mtry min_n .config              
  <int> <int> <chr>                
1     4     4      Preprocessor1_Model08

#Plot AUC
rf_auc <- 
  rf_res %>% 
  collect_predictions(parameters = rf_best) %>% 
  roc_curve(isWinner, .pred_0) %>% 
  mutate(model = "Random Forest")

autoplot(rf_auc)

10) Create the final model with the best parameters

11) Execute the final fit

12) Plot feature importance, The bowler and batsman embedding followed by perfIndex and runRate are features that contribute the most to the Win Probability

last_rf_mod <- 
  rand_forest(mtry = 4, min_n = 4, trees = 1000) %>% 
  set_engine("ranger", num.threads = cores, importance = "impurity") %>% 
  set_mode("classification")

# the last workflow
last_rf_workflow <- 
  rf_workflow %>% 
  update_model(last_rf_mod)

set.seed(345)
last_rf_fit <- 
  last_rf_workflow %>% 
  last_fit(splits)

last_rf_fit %>% 
  collect_metrics()

  .metric  .estimator .estimate .config             
  <chr>    <chr>          <dbl> <chr>               

1 accuracy binary         0.944 Preprocessor1_Model1
2 roc_auc  binary         0.988 Preprocessor1_Model1

last_rf_fit %>% 
  extract_fit_parsnip() %>% 
  vip(num_features = 9)

13) Plot the ROC curve for the best fit

# Plot the ROC for the final model
last_rf_fit %>% 
  collect_predictions() %>% 
  roc_curve(isWinner, .pred_0) %>% 
  autoplot()

14) Create a confusion matrix

We can see that the number of false positives and false negatives is very low

15) Create the final fit with the Random Forest Model

# generate predictions from the test set
test_predictions <- last_rf_fit %>% collect_predictions()
test_predictions

   id               .pred_0 .pred_1  .row .pred_class isWinner .config          
   <chr>              <dbl>   <dbl> <int> <fct>       <fct>    <chr>            
 1 train/test split   0.838  0.162      1 0           0       Preprocessor1_Mo…
 2 
train/test split   0.463  0.537     11 1           0        Preprocessor1_Mo…
 3 
train/test split   0.846  0.154     14 0           0        Preprocessor1_Mo…
 4 
train/test split   0.839  0.161     22 0           0        Preprocessor1_Mo…
 5 
train/test split   0.846  0.154     36 0           0        Preprocessor1_Mo…
 6 
train/test split   0.848  0.152     37 0           0        Preprocessor1_Mo…
 7 
train/test split   0.731  0.269     39 0           0        Preprocessor1_Mo…
 8 
train/test split   0.972  0.0281    40 0           0        Preprocessor1_Mo…
 9 
train/test split   0.655  0.345     42 0           0        Preprocessor1_Mo…
10 
train/test split   0.662  0.338     43 0           0        Preprocessor1_Mo…

# generate a confusion matrix
test_predictions %>% 
  conf_mat(truth = isWinner, estimate = .pred_class)

          Truth
Prediction      0      1
         
          0 116576   7096
         
          1   6391 109760

# Create the final model
final_model <- fit(last_rf_workflow, df_other)

16) Computing Win Probability with Random Forest Model for match

  • Pakistan-India-2022-10-23

17) Worm -wicket graph of match

  • Pakistan-India-2022-10-23

C) Win Probability using MLP – Deep Neural Network (DNN) with player embeddings

In this approach the MLP package of Tidymodels was used. Multi-layer perceptron (MLP) with Deep Neural Network (DNN) was used to compute the Win Probability using player embeddings. An accuracy of 0.76 was obtained

1) Read the data

a) Read the data from 9 T20 leagues (BBL, CPL, IPL, NTB, PSL, SSM, T20 Men, T20 Women, WBB) and create a single data frame of ball-by-ball data. Display the data frame

2) Create training.validation and test sets

b) Split to training, validation and test sets. The dataset is initially split into training and test in the ratio 80%:20%. The training data is again split into training and validation in the ratio 80:20

library(dplyr)
library(caret)
library(e1071)
library(ggplot2)
library(tidymodels)    
library(embed)

# Helper packages
library(readr)       # for importing data
library(vip) 
library(ranger)

df1=read.csv("output3/matchesBBL3.csv")
df2=read.csv("output3/matchesCPL3.csv")
df3=read.csv("output3/matchesIPL3.csv")
df4=read.csv("output3/matchesNTB3.csv")
df5=read.csv("output3/matchesPSL3.csv")
df6=read.csv("output3/matchesSSM3.csv")
df7=read.csv("output3/matchesT20M3.csv")
df8=read.csv("output3/matchesT20W3.csv")
df9=read.csv("output3/matchesWBB3.csv")

df=rbind(df1,df2,df3,df4,df5,df6,df7,df8,df9)


set.seed(123)
df$isWinner = as.factor(df$isWinner)
splits      <- initial_split(df,prop = 0.80)
df_other <- training(splits)
df_test  <- testing(splits)
set.seed(234)
val_set <- validation_split(df_other, 
                            prop = 0.80)
val_set

3) Create a Deep Neural Network recipe

  • Normalize parameters
  • Add embeddings for batsman, bowler

4) Set the MLP-DNN hyperparameters

  • epochs=100
  • hidden units =5
  • dropout regularization =0.1

5) Fit on Training data

cores <- parallel::detectCores()
cores

nn_recipe <- 
  recipe(isWinner ~ ., data = df_other) %>% 
step_normalize(ballNum,ballsRemaining,runs,runRate,numWickets,runsMomentum,perfIndex) %>%
  step_embed(batsman,bowler, outcome = vars(isWinner)) %>%
  prep(training = df_other, retain = TRUE) 

# For validation:
test_normalized <- bake(nn_recipe, new_data = df_test)

set.seed(57974)
# Set the hyper parameters for DNN
# Use Keras
# Fit on training data
nnet_fit <-
  mlp(epochs = 100, hidden_units = 5, dropout = 0.1) %>%
  set_mode("classification") %>% 
  # Also set engine-specific `verbose` argument to prevent logging the results: 
  set_engine("keras", verbose = 0) %>%
  fit(isWinner ~ ., data = bake(nn_recipe, new_data = df_other))

nnet_fit
parsnip model object
Model:"sequential"

____________________________________________________________________________

Layer (type)                                           Output Shape                                    Param #            
============================================================================
dense (Dense)                                           (None, 5)                                          60                 
____________________________________________________________________________

dense_1 (Dense)                                         (None, 5)                                          30                 
____________________________________________________________________________
dropout (Dropout)                                       (None, 5)                                          0                  
____________________________________________________________________________
dense_2 (Dense)                                         (None, 2)                                          12                 
============================================================================
Total params: 102
Trainable params: 102
Non-trainable params: 0

6) Test on Test data

  • Check ROC_AUC. It is 0.854
  • Check accuracy. The MLP-DNN gives a decent performance with an acuracy of 0.76
  • Compute the Confusion Matrix
# Validate on test data
val_results <- 
  df_test %>%
  bind_cols(
    predict(nnet_fit, new_data = test_normalized),
    predict(nnet_fit, new_data = test_normalized, type = "prob")
  )
val_results 

# Check roc_auc
val_results %>% roc_auc(truth = isWinner, .pred_0)
  .metric .estimator .estimate
  
   <chr>   <chr>          <dbl>
1 roc_auc binary         0.854

# Check accuracy
val_results %>% accuracy(truth = isWinner, .pred_class)
  .metric  .estimator .estimate
  <chr>    <chr>          <dbl>
1 accuracy binary         0.762

# Display confusion matrix
val_results %>% conf_mat(truth = isWinner, .pred_class)
          Truth
Prediction     
           0     1        
       0 97419 31564       
       1 25548 85292

Conclusion

  1. Of the 3 ML models, glmnet, random forest and Multi-layer Perceptron DNN, random forest had the best performance
  2. Random Forest ML model with batsman, bowler embeddings was able to achieve an accuracy of 92.4% and a ROC_AUC of 0.98 with very low false positives, negatives. This was a quantum jump from my earlier random forest model without embeddings which had an accuracy of 73.7% and an ROC_AUC of 0.834
  3. The glmnet and NN models are fairly light weight. Random Forest is computationally very intensive.

Check out my other posts

  1. Using Reinforcement Learning to solve Gridworld
  2. Deep Learning from first principles in Python, R and Octave – Part 8
  3. Introducing QCSimulator: A 5-qubit quantum computing simulator in R
  4. Big Data-5: kNiFi-ing through cricket data with yorkpy
  5. Singularity
  6. Practical Machine Learning with R and Python – Part 6
  7. GooglyPlusPlus2022 optimizes batting/bowling lineup
  8. Fun simulation of a Chain in Android
  9. Introducing cricpy:A python package to analyze performances of cricketers
  10. Programming languages in layman’s language

To see all posts click Index of posts

Computing Win-Probability of T20 matches

I am late to the ‘Win probability’ computation for T20 matches, but managed to jump on to this bus with this post. Win Probability analysis and computation have been around for some time and are used in baseball, NFL, soccer hockey and others. On T20 cricket, the following posts from White Ball Analytics & Sports Data Science were good pointers to the general approach. The data for the Win Probability computation is taken from Cricsheet.

My initial Machine Learning models could not do better than 62% accuracy. I created a data set of ~830 IPL matches which roughly came to about 280,000 rows of ball-by-ball match data but I could not move beyond 62%. Addition of T20 men moved the needle to 64% accuracy. I spent time tuning Deep Learning networks using Tensorflow and Keras. Finally, I added T20 data from 9 T20 leagues – IPL, T20 men, T20 women, BBL, CPL, NTB, PSL, WBB, SSM. I had one large data set of 1.2 million rows of ball by ball data. The data frame looks like

I created a data frame for each match from ball Num 1 to ballNum ~240 for the 1st and 2nd innings of the match. My initial set of features were ballNum, runs, runRate, numWickets. The target variable isWinner= {0,1} depending on whether the team has won or lost the match.

The features

  • ballNum – ball number for 1 ~ 240+ in data frame. 1 – 120+ for 1st innings and 120+ – 240+ in 2nd innings including noballs, wides etc.
  • runs = cumulative runs scored at the ball count
  • runRate = cumulative runs scored/ ballNum (for 1st innings) and runs= required runs/ball Num for 2nd innings
  • numWickets = wickets lost

The target variable isWinner can take values {0,1} depending whether the team won or lost

With this initial dataframe, even though I had close to 1.2 million rows of ball by ball data of T20 matches my best performance with vanilla Logistic regression & SVM in Python was about 64% accuracy.

# Read all the data from 9 T20 leagues
# BBL,CPL, IPL, NTB, PSL, SSM, T20 Men, T20 Women, WBB
df1=pd.read_csv('matchesT20M.csv')
df2=pd.read_csv('matchesIPL.csv')
df3=pd.read_csv('matchesBBL.csv')
df4=pd.read_csv('matchesCPL.csv')
df5=pd.read_csv('matchesNTB.csv')
df6=pd.read_csv('matchesPSL.csv')
df7=pd.read_csv('matchesSSM.csv')
df8=pd.read_csv('matchesT20W.csv')
df9=pd.read_csv('matchesWBB.csv')

# Create one large dataframe
df10=pd.concat([df1,df2,df3,df4,df5,df6,df7,df8,df9])
print("Shape of dataframe=",df10.shape)
print("#####################################")
stats=check_values(df10)
print("#####################################")
model_fit(df10)
#norm_model_fit(df,stats)
svm_model_fit(df10)

Shape of dataframe= (1206901, 6)
#####################################
Null values: False
It contains 0 infinite values

Accuracy of Logistic regression classifier on training set: 0.63
Accuracy of Logistic regression classifier on test set: 0.64
Accuracy: 0.64
Precision: 0.62
Recall: 0.65
F1: 0.64


Accuracy of Linear SVC classifier on training set: 0.52
Accuracy of Linear SVC classifier on test set: 0.52

With Tensorflow/Keras the performance was about 67%. I tried several things

  • Normalisation
  • Tried different learning rates
  • Different optimisers – SGD, RMSProp, Adam
  • Changed depth and width of Neural Network

However I did not get much improvement. Finally I decided to do some Feature engineering. I added 2 new features

a) Runs Momentum : This feature is based on the fact that more the wickets in hand, the more freely the batsmen can make risky strokes, hence increasing the momentum of the runs, This is calculated as

runsMomentum = (11 – numWickets)/balls remaining

b) Performance Index: This feature is the product of the run rate x wickets in hand. In other words, if the strike rate is good and fewer wickets lost at the point in the match, then the performance index is higher at that point in the match will be higher

The final set of features chosen were as below

I had also included the balls Remaining in the innings. Now with this set of features I decided to execute Tensorflow/Keras and do a GridSearch with different learning rates, optimisers. After a couple of hours of computation I got an accuracy of 0.73. I needed to be able to read the ML model in R which required installation of Tensorflow, reticulate and Keras in RStudio and I had several issues. Since I hit a roadblock I moved to regular R models

I performed WIn Probability computation in the following ways

A) Win Probability with Vanilla Logistic Regression (R)

With vanilla Logistic Regression in R using the ‘glm’ package I got an accuracy of 0.67, sensitivity of 0.68 and specificity of 0.65 as shown below

library(dplyr)
library(caret)
library(e1071)
library(ggplot2)

# Read all the data from 9 T20 leagues
# BBL,CPL, IPL, NTB, PSL, SSM, T20 Men, T20 Women, WBB
df1=read.csv("output2/matchesBBL2.csv")
df2=read.csv("output2/matchesCPL2.csv")
df3=read.csv("output2/matchesIPL2.csv")
df4=read.csv("output2/matchesNTB2.csv")
df5=read.csv("output2/matchesPSL2.csv")
df6=read.csv("output2/matchesSSM2.csv")
df7=read.csv("output2/matchesT20M2.csv")
df8=read.csv("output2/matchesT20W2.csv")
df9=read.csv("output2/matchesWBB2.csv")

# Create one large dataframe
df=rbind(df1,df2,df3,df4,df5,df6,df7,df8,df9)

# Helper function to split into training/test
trainTestSplit <- function(df,trainPercent,seed1){
  ## Sample size percent
  samp_size <- floor(trainPercent/100 * nrow(df))
  ## set the seed 
  set.seed(seed1)
  idx <- sample(seq_len(nrow(df)), size = samp_size)
  idx
  
}

train_idx <- trainTestSplit(df,trainPercent=80,seed=5)
train <- df[train_idx, ]

test <- df[-train_idx, ]
# Fit a generalized linear logistic model, 
fit=glm(isWinner~.,family=binomial,data=train,control = list(maxit = 50))

a=predict(fit,newdata=train,type="response")
# Set response >0.5 as 1 and <=0.5 as 0
b=as.factor(ifelse(a>0.5,1,0))
# Compute the confusion matrix for training data

confusionMatrix(
  factor(b, levels = 0:1),
  factor(train$isWinner, levels = 0:1)
)

Confusion Matrix and Statistics

          Reference
Prediction    
  0      1
         0 339938 160336
         1 154236 310217
                                         
               Accuracy : 0.6739         
                 95% CI : (0.673, 0.6749)
    No Information Rate : 0.5122         
    P-Value [Acc > NIR] : < 2.2e-16      
                                         
                  Kappa : 0.3473         
                                         
 Mcnemar's Test P-Value : < 2.2e-16      
                                         
            Sensitivity : 0.6879         
            Specificity : 0.6593         
         Pos Pred Value : 0.6795         
         Neg Pred Value : 0.6679         
             Prevalence : 0.5122         
         Detection Rate : 0.3524         
   Detection Prevalence : 0.5186         
      Balanced Accuracy : 0.6736         
                                         
       'Positive' Class : 0      

# This can be saved and loaded as    
saveRDS(fit, "glm.rds")
ml_model <- readRDS("glm.rds")    

Using the above ML model on Deccan Chargers vs Chennai Super on 27-04-2009 the Win Probability as the match progresses is as below

The Worm wicket graph of this match shows it was a closely fought match

B) Win Probability using Random Forests with Tidy Models – R

Initially I tried Tidy models with tuning for glmnet. The best I got was 0.67. However, I got an excellent performance using TidyModels with Random Forests. I am using Tidy Models for the first time and I have been blown away with how logically it is constructed, much like dplyr & ggplot2.

library(dplyr)
library(caret)
library(e1071)
library(ggplot2)
library(tidymodels)  

# Helper packages
library(readr)       # for importing data
library(vip) 
library(ranger)
# Read all the data from 9 T20 leagues
# BBL,CPL, IPL, NTB, PSL, SSM, T20 Men, T20 Women, WBB

df1=read.csv("output2/matchesBBL2.csv")
df2=read.csv("output2/matchesCPL2.csv")
df3=read.csv("output2/matchesIPL2.csv")
df4=read.csv("output2/matchesNTB2.csv")
df5=read.csv("output2/matchesPSL2.csv")
df6=read.csv("output2/matchesSSM2.csv")
df7=read.csv("output2/matchesT20M2.csv")
df8=read.csv("output2/matchesT20W2.csv")
df9=read.csv("output2/matchesWBB2.csv")

# Create one large dataframe
df=rbind(df1,df2,df3,df4,df5,df6,df7,df8,df9)

dim(df)
[1] 
1205909       8

# Take a peek at the dataset
glimpse(df)
$ ballNum        <int> 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28…
$ ballsRemaining <int> 125, 124, 123, 122, 121, 120, 119, 118, 117, 116, 115, 114, 113, 112, 111, 110, 109, 108, 107, 106, 1…
$ runs           <int> 1, 1, 2, 3, 3, 3, 4, 4, 5, 5, 6, 7, 13, 14, 16, 18, 18, 18, 24, 24, 24, 26, 26, 32, 32, 33, 34, 34, 3…
$ runRate        <dbl> 1.0000000, 0.5000000, 0.6666667, 0.7500000, 0.6000000, 0.5000000, 0.5714286, 0.5000000, 0.5555556, 0.…
$ numWickets     <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3,…
$ runsMomentum   <dbl> 0.08800000, 0.08870968, 0.08943089, 0.09016393, 0.09090909, 0.09166667, 0.09243697, 0.09322034, 0.094…
$ perfIndex      <dbl> 11.000000, 5.500000, 7.333333, 8.250000, 6.600000, 5.500000, 6.285714, 5.500000, 6.111111, 5.000000, …
$ isWinner       <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,…

df %>% 
  count(isWinner) %>% 
  mutate(prop = n/sum(n))

set.seed(123)
df$isWinner = as.factor(df$isWinner)

# Split the data into training and test set in 80%:20%
splits      <- initial_split(df,prop = 0.80)
df_other <- training(splits)
df_test  <- testing(splits)

# Create a validation set from training set in 80%:20%
set.seed(234)
val_set <- validation_split(df_other, 
                            prop = 0.80)
val_set

# Setup for Random forest using Ranger for classification
# Set up cores for parallel execution
cores <- parallel::detectCores()
cores

#Set up Random Forest engine
rf_mod <- 
  rand_forest(mtry = tune(), min_n = tune(), trees = 1000) %>% 
  set_engine("ranger", num.threads = cores) %>% 
  set_mode("classification")

rf_mod
# The Random Forest engine includes mtry which is number of predictor 
# variables required at each decision  tree with min_n the minimum number # of 
Random Forest Model Specification (classification)

Main Arguments:
  mtry = tune()
  trees = 1000
  min_n = tune()

Engine-Specific Arguments:
  num.threads = cores

Computational engine: ranger


# Setup the predictors and target variable
# Normalise all predictors. Random Forest don't need normalization but
# I have done it anyway
rf_recipe <-
  recipe(isWinner ~ ., data = df_other) %>% 
  step_normalize(all_predictors())

# Create workflow adding the ML model and recipe
rf_workflow <- 
  workflow() %>% 
  add_model(rf_mod) %>% 
  add_recipe(rf_recipe)

# The tune is done for 5 different values of the tuning parameters.
# Metrics include accuracy and roc_auc
rf_res <- 
  rf_workflow %>% 
  tune_grid(val_set,
            grid = 5,
            control = control_grid(save_pred = TRUE),
            metrics = metric_set(accuracy,roc_auc))

$ Pick the best of ROC/AUC
rf_res %>% 
  show_best(metric = "roc_auc")

We can see that when mtry (number of predictors) is 5 or 7 the ROC_AUC is 0.834 which is quite good

# A tibble: 5 × 8
   mtry min_n .metric .estimator  mean     n std_err .config             
  <int> <int> <chr>   <chr>      <dbl> <int>   <dbl> <chr>               
1     5    26 roc_auc binary     0.834     1      NA Preprocessor1_Model5
2     7    36 roc_auc binary     0.834     1      NA Preprocessor1_Model3
3     2    17 roc_auc binary     0.833     1      NA Preprocessor1_Model4
4     1    20 roc_auc binary     0.832     1      NA Preprocessor1_Model2
5     5     6 roc_auc binary     0.825     1      NA Preprocessor1_Model1


# Select the model with highest accuracy
rf_res %>% 
  show_best(metric = "accuracy")
   mtry min_n .metric  .estimator  mean     n std_err .config             
  <int> <int> <chr>    <chr>      <dbl> <int>   <dbl> <chr>               
1     7    36 accuracy binary     0.737     1      NA Preprocessor1_Model3
2     5    26 accuracy binary     0.736     1      NA Preprocessor1_Model5
3     1    20 accuracy binary     0.736     1      NA Preprocessor1_Model2
4     2    17 accuracy binary     0.735     1      NA Preprocessor1_Model4
5     5     6 accuracy binary     0.731     1      NA Preprocessor1_Model1

# The model with mtry (number of predictors) is 7 has the best accuracy. 
# Hence the best model has mtry=7 and min_n=36

rf_best <- 
  rf_res %>% 
  select_best(metric = "accuracy")

# Display the best model
rf_best
# A tibble: 1 × 3
   mtry min_n .config             
  <int> <int> <chr>               
1     7    36 Preprocessor1_Model3


rf_res %>% 
  collect_predictions()
   id         .pred_class  .row  mtry min_n .pred_0  .pred_1 isWinner .config             
   <chr>      <fct>       <int> <int> <int>   <dbl>    <dbl> <fct>    <chr>               
 1 validation 1               1     5     6 0.497   0.503    0        Preprocessor1_Model1
 2 validation 1               9     5     6 0.00753 0.992    1        Preprocessor1_Model1
 3 validation 0              10     5     6 0.627   0.373    0        Preprocessor1_Model1
 4 validation 0              16     5     6 0.998   0.002    0        Preprocessor1_Model1
 5 validation 1              18     5     6 0.270   0.730    1        Preprocessor1_Model1
 6 validation 0              23     5     6 0.899   0.101    0        Preprocessor1_Model1
 7 validation 1              26     5     6 0.452   0.548    1        Preprocessor1_Model1
 8 validation 0              30     5     6 0.657   0.343    1        Preprocessor1_Model1
 9 validation 0              34     5     6 0.576   0.424    0        Preprocessor1_Model1
10 validation 0              35     5     6 1.00    0.000167 0        Preprocessor1_Model1

rf_auc <- 
  rf_res %>% 
  collect_predictions(parameters = rf_best) %>% 
  roc_curve(isWinner, .pred_0) %>% 
  mutate(model = "Random Forest")

autoplot(rf_auc)

I

The Final Model

# Create the final Random Forest model with mtry=7 and min_n=36
# engine as "ranger" for classification
last_rf_mod <- 
  rand_forest(mtry = 7, min_n = 36, trees = 1000) %>% 
  set_engine("ranger", num.threads = cores, importance = "impurity") %>% 
  set_mode("classification")


# the last workflow is updated with the final model
last_rf_workflow <- 
  rf_workflow %>% 
  update_model(last_rf_mod)

set.seed(345)
last_rf_fit <- 
  last_rf_workflow %>% 
  last_fit(splits)

# Collect metrics
last_rf_fit %>% 
  collect_metrics()
  .metric  .estimator .estimate .config             
  <chr>    <chr>          <dbl> <chr>               
1 accuracy binary         0.739 Preprocessor1_Model1
2 roc_auc  binary         0.837 Preprocessor1_Model1

The Random Forest model gives an accuracy of 0.739 and ROC_AUC of .837 which I think is quite good. This is roughly what I got with Tensorflow/Keras

# Get the feature importance 
last_rf_fit %>% 
  extract_fit_parsnip() %>% 
  vip(num_features = 7)

Interestingly the feature that I engineered seems to have the maximum importancce namely Performance Index which is a product of Run rate x Wicket in Hand. I would have thought numWickets would be important but in T20 match probably is is not.

 generate predictions from the test set
test_predictions <- last_rf_fit %>% collect_predictions()
> test_predictions
# A tibble: 241,182 × 7
id               .pred_0 .pred_1  .row .pred_class isWinner .config             
<chr>              <dbl>   <dbl> <int> <fct>       <fct>    <chr>               
  1 train/test split   0.496   0.504     1 1           0        Preprocessor1_Model1
2 train/test split   0.640   0.360    11 0           0        Preprocessor1_Model1
3 train/test split   0.596   0.404    14 0           0        Preprocessor1_Model1
4 train/test split   0.287   0.713    22 1           0        Preprocessor1_Model1
5 train/test split   0.616   0.384    28 0           0        Preprocessor1_Model1
6 train/test split   0.516   0.484    36 0           0        Preprocessor1_Model1
7 train/test split   0.754   0.246    37 0           0        Preprocessor1_Model1
8 train/test split   0.641   0.359    39 0           0        Preprocessor1_Model1
9 train/test split   0.811   0.189    40 0           0        Preprocessor1_Model1
10 train/test split   0.618   0.382    42 0           0        Preprocessor1_Model1


# generate a confusion matrix
test_predictions %>% 
  conf_mat(truth = isWinner, estimate = .pred_class)

          Truth
Prediction     0     1
         0 92173 31623
         1 31320 86066

# Create the final model on the train/test data
final_model <- fit(last_rf_workflow, df_other)

# Final model
final_model
══ Workflow [trained] ════════════════════════════════════════════════════════════════════════════════════════════════════════
Preprocessor: Recipe
Model: rand_forest()

── Preprocessor ──────────────────────────────────────────────────────────────────────────────────────────────────────────────
1 Recipe Step

• step_normalize()

── Model ─────────────────────────────────────────────────────────────────────────────────────────────────────────────────────
Ranger result

Call:
 ranger::ranger(x = maybe_data_frame(x), y = y, mtry = min_cols(~7,      x), num.trees = ~1000, min.node.size = min_rows(~36, x),      num.threads = ~cores, importance = ~"impurity", verbose = FALSE,      seed = sample.int(10^5, 1), probability = TRUE) 

Type:                             Probability estimation 
Number of trees:                  1000 
Sample size:                      964727 
Number of independent variables:  7 
Mtry:                             7 
Target node size:                 36 
Variable importance mode:         impurity 
Splitrule:                        gini 
OOB prediction error (Brier s.):  0.1631303

The Random Forest Model’s performance has been quite impressive and probably requires further exploration.

# Saving and loading the model
save(final_model, file = "fit.rda")
load("fit.rda")

#Predicting the Win Probability of CSK vs DD match on 12 May 2012

Comparing this with the Worm wicket graph of this match we see that DD had no chance at all

C) Win Probability with Tensorflow/Keras with Grid Search – Python

I spent a fair amount of time tuning the hyper parameters of the Keras Deep Learning Network. Finally did go for the Grid Search. Incidentally I did ask ChatGPT to suggest code snippets for GridSearch which it promptly did!!!

import pandas as pd
import numpy as np
from zipfile import ZipFile
import tensorflow as tf
from tensorflow import keras
from tensorflow.keras import layers
from tensorflow.keras import regularizers
from sklearn.model_selection import GridSearchCV

# Define the model
def create_model(optimizer='adam'):
    tf.random.set_seed(4)
    model = tf.keras.Sequential([
        keras.layers.Dense(32, activation=tf.nn.relu, input_shape=[len(train_dataset1.keys())]),
        keras.layers.Dense(16, activation=tf.nn.relu),
        keras.layers.Dense(8, activation=tf.nn.relu),
        keras.layers.Dense(1,activation=tf.nn.sigmoid)
    ])

    # Since this is binary classification use binary_crossentropy
    model.compile(loss='binary_crossentropy',
                    optimizer=optimizer,
                    metrics='accuracy')
    return(model)

    # Create a KerasClassifier object
model = keras.wrappers.scikit_learn.KerasClassifier(build_fn=create_model)

# Define the grid of hyperparameters to search over
batch_size = [1024]
epochs = [40]
learning_rate = [0.01, 0.001, 0.0001]
optimizer = ['SGD', 'RMSprop', 'Adagrad', 'Adadelta', 'Adam', 'Adamax', 'Nadam']

param_grid = dict(dict(optimizer=optimizer,batch_size=batch_size, epochs=epochs) )
# Create the grid search object
grid_search = GridSearchCV(estimator=model, param_grid=param_grid, cv=3)

# Fit the grid search object to the training data
grid_search.fit(normalized_train_data, train_labels)

# Print the best hyperparameters
print('Best hyperparameters:', grid_search.best_params_)
# summarize results
print("Best: %f using %s" % (grid_search.best_score_, grid_search.best_params_))
means = grid_search.cv_results_['mean_test_score']
stds = grid_search.cv_results_['std_test_score']
params = grid_search.cv_results_['params']
for mean, stdev, param in zip(means, stds, params):
    print("%f (%f) with: %r" % (mean, stdev, param))

The best worked out to be the optimiser ‘Nadam’ with a learning rate of 0.001

import matplotlib.pyplot as plt
# Create a model
tf.random.set_seed(4)
model = tf.keras.Sequential([
    keras.layers.Dense(32, activation=tf.nn.relu, input_shape=[len(train_dataset1.keys())]),
    keras.layers.Dense(16, activation=tf.nn.relu),
    keras.layers.Dense(8, activation=tf.nn.relu),
    keras.layers.Dense(1,activation=tf.nn.sigmoid)
  ])

# Use the Nadam optimiser
optimizer=keras.optimizers.Nadam(learning_rate=.001, beta_1=0.9, beta_2=0.999, epsilon=1e-07, decay=0.0)

# Since this is binary classification use binary_crossentropy
model.compile(loss='binary_crossentropy',
                optimizer=optimizer,
                metrics='accuracy')

# Fit 
#history=model.fit(
#  train_dataset1, train_labels,batch_size=1024,
#  epochs=40, validation_data=(test_dataset1,test_labels), verbose=1)
history=model.fit(
  normalized_train_data, train_labels,batch_size=1024,
  epochs=40, validation_data=(normalized_test_data,test_labels), verbose=1)

Epoch 37/40
943/943 [==============================] - 3s 3ms/step - loss: 0.4971 - accuracy: 0.7310 - val_loss: 0.4968 - val_accuracy: 0.7357
Epoch 38/40
943/943 [==============================] - 3s 3ms/step - loss: 0.4970 - accuracy: 0.7310 - val_loss: 0.4974 - val_accuracy: 0.7378
Epoch 39/40
943/943 [==============================] - 4s 4ms/step - loss: 0.4970 - accuracy: 0.7309 - val_loss: 0.4994 - val_accuracy: 0.7296
Epoch 40/40
943/943 [==============================] - 3s 3ms/step - loss: 0.4969 - accuracy: 0.7311 - val_loss: 0.4998 - val_accuracy: 0.7300
plt.plot(history.history["loss"])
plt.plot(history.history["val_loss"])
plt.title("model loss")
plt.ylabel("loss")
plt.xlabel("epoch")
plt.legend(["train", "test"], loc="upper left")
plt.show()

Conclusion

So, the Keras Deep Learning Network gives about the same performance of Random Forest in Tidy Models. But I went with R Random Forest as it was easier to save and load the model for use with my data. Also, I am not sure whether the performance of the ML model can be improved beyond a point. However, I will continue to explore.

Watch this space!!!

Also see

  1. Natural language processing: What would Shakespeare say?
  2. Revisiting World Bank data analysis with WDI and gVisMotionChart
  3. The mechanics of Convolutional Neural Networks in Tensorflow and Keras
  4. Deep Learning from first principles in Python, R and Octave – Part 4
  5. Big Data-4: Webserver log analysis with RDDs, Pyspark, SparkR and SparklyR
  6. Latency, throughput implications for the Cloud
  7. Practical Machine Learning with R and Python – Part 4
  8. Pitching yorkpy…swinging away from the leg stump to IPL – Part 3
  9. Experiments with deblurring using OpenCV
  10. Design Principles of Scalable, Distributed Systems

To see all posts click Index of posts

References

  1. White Ball Analytics
  2. Twenty20 Win Probability Added
  3. Tidy models – A predictive modeling case study
  4. Tidymodels: tidy machine learning in R
  5. A gentle introduction to Tidy models
  6. How to Grid Search Hyperparameters for Deep Learning Models in Python with Keras
  7. ChatGPT

Using embeddings, collaborative filtering with Deep Learning to analyse T20 players

There is a school of thought which considers that total runs scored and strike rate for a batsman, or total wickets taken and economy rate for a bowler, do not tell the whole story. This is true to a fair extent. The runs scored or the wickets taken could have been against weaker teams and hence the runs, strike rate or the wickets and economy rate alone do not capture all the performance details of the batsman or bowler. A technique to determine the performance of batsmen against different bowlers and identify the batsman’s possible performance even against bowlers he/she has not yet faced could be done with collaborative filtering. Collaborative filtering, with embeddings can also be used to group players with similar characteristics. Similarly, we could also identify the performance of bowlers versus different batsmen. Hence we need to look at average runs, SR and total wickets, ER with the lens of batsmen, bowlers against similar opposition. This is where collaborative filtering is useful.

The table below shows the performance of all batsman against all bowlers in the table below. The row in the table below is the batsman and the column is the bowler, with the value in the cell is the total Runs scored by the batsman against the bowler in all matches. Note the values are 0 for batsmen who have not yet faced specific bowlers. The table is fairly sparse.

Table A

Similarly, we can compute the performance of all bowlers against all batsmen as in the table below. Here the row is the bowler, the column batsman and the value in the cell is the number of times the bowler got the batsman’s wicket. As before the data is sparsely populated

This problem of computing batsman’s performance against bowlers or vice versa, is identical to the user vs movie rating problem used in collaborative filtering. For e.g we could consider

This above problem depicted could be computed using collaborative filtering with embeddings. We could assign sequential numbers for the batsmen from 1 to M, and for the bowlers from 1 to N. The total runs scored could be represented only for the rows where there are values. One way to solve this problem in Machine Learning is to use One Hot Encoding (OHE), where we assign values for each row and each column and map the values of the table with values of the cell for each combination. But this would take a enormous computation time and memory. The solution to this is use vector embeddings. Here embeddings could be used for capturing the sparse tensors between the batsmen, bowlers, runs scored or vice versa between bowlers against batsmen and the wickets taken. We only need to consider the cells for which values exist. An embedding is a relatively low-dimensional space, into which you can translate high-dimensional vectors. An embedding captures some of the semantics of the input by placing semantically similar inputs close together in the embedding space.

a) To compute bowler performances and identify similarities between bowlers the following embedding in the Deep Learning Network was used

To compute batsmen similarities a similar Deep Learning network for bowler vs batsmen is used

I had earlier created another post Player Performance Estimation using AI Collaborative Filtering for batsman and bowler recommendation, using R package Recommender Lab. However, I was not too happy with the results I got with this R package. When I searched the net for material on using embeddings for collaborative filtering, most of material on the web on movie lens or word2vec are repetitive and have no new material. Finally, this short video lecture from Developer Google on Embeddings provided the most clarity.

I have created 4 Colab notebooks to identify player similarities (recommendations)

a) Batsman similarities IPL

b) Batsman similarities T20

c) Bowler similarities IPL

d) Bowler similarities T20

For creating the model I have used all the data for T20 and IPL from so that I get the best results. The data is from Cricsheet. I have also used Google’s Embeddings Projector to display batsman and bowler embedding to and to group similar players

All the Colab notebooks and the data associated with the code are available in Github. Feel free to download and execute them. See if you get better performance. I tried a wide variety of hyperparameters – learning rate, width and depth of nodes per layer, number of layers, gradient methods etc.

You can download all the code & data from Github at embeddings

A) Batsman Recommender IPL (BatsmanRecommenderIPLA.ipynb)

Steps for creating the model

a) Upload bowler vs batsmen with times wicket was taken for batsman. This will be a sparse matrix

b) Assign integer indices for bowlers, batsmen

c) Add additional input features balls, runs conceded and Economy rate

d) Minimise loss for wickets taken for the bowler using SGD

e) Display embeddings of similar batsmen using Tensorboard projector

a) Upload data

Upload data file
2. Remove rows where wickets = 0

from google.colab import files
import io
uploaded = files.upload()
df2 = pd.read_csv(io.BytesIO(uploaded['bowlerVsBatsmanIPLE.csv']))
print(df2.shape)
df2 = df2.loc[df2['wicketTaken']!= 0]
print(df2.shape)

uploaded = files.upload()
df6 = pd.read_csv(io.BytesIO(uploaded['bowlerVsBatsmanIPLAll.csv']))
df6
     


Out[14]:

bowler1batsman1ballsrunsConcededER
0A Ashish ReddyDJG Sammy100.000000
1A Ashish ReddyG Gambhir101710.200000
2A Ashish ReddyJEC Franklin200.000000
3A Ashish ReddyLRPL Taylor567.200000
4A Ashish ReddyMA Agarwal3714.000000
8550Z KhanVishnu Vinod4812.000000
8551Z KhanVS Malik3510.000000
8552Z KhanW Jaffer732.571429
8553Z KhanYK Pathan22359.545455
8554Z KhanYuvraj Singh12126.000000

b) Create integer dictionaries for batsmen & bowlers

bowlers = df3["bowler1"].unique().tolist()
bowlers
# Create dictionary of bowler to index
bowlers2index = {x: i for i, x in enumerate(bowlers)}
bowlers2index
#Create dictionary of index tp bowler
index2bowlers = {i: x for i, x in enumerate(bowlers)}
index2bowlers


batsmen = df3["batsman1"].unique().tolist()
batsmen
# Create dictionary of batsman to index
batsmen2index = {x: i for i, x in enumerate(batsmen)}
batsmen2index
# Create dictionary of index to batsman
index2batsmen = {i: x for i, x in enumerate(batsmen)}
index2batsmen

#Map bowler, batsman to respective indices
df3["bowler"] = df3["bowler1"].map(bowlers2index)
df3["batsman"] = df3["batsman1"].map(batsmen2index)
df3
num_bowlers =len(bowlers2index)
num_batsmen = len(batsmen2index)
df3["wicketTaken"] = df3["wicketTaken"].values.astype(np.float32)
df3
# min and max ratings will be used to normalize the ratings later
min_wicketTaken = min(df3["wicketTaken"])
max_wicketTaken = max(df3["wicketTaken"])

print(
    "Number of bowlers: {}, Number of batsmen: {}, Min wicketsTaken: {}, Max wicketsTaken: {}".format(
        num_bowlers, num_batsmen, min_wicketTaken, max_wicketTaken
    )
)

c) Concatenate additional features

df3
df6
df31=pd.concat([df3,df6],axis=1)
df31

d) Create a Tensorflow/Keras deep learning mode. Minimise using Mean Squared Error using Stochastic Gradient Descent. I used ‘dropouts’ to regularise the model to keep validation loss within limits

tf.random.set_seed(4)
vector_size=len(batsmen2index)

df4=df31[['bowler','batsman','wicketTaken','balls','runsConceded','ER']]
df4
train_dataset = df4.sample(frac=0.9,random_state=0)
test_dataset = df4.drop(train_dataset.index)

train_dataset1 = train_dataset[['bowler','batsman','balls','runsConceded','ER']]
test_dataset1 = test_dataset[['bowler','batsman','balls','runsConceded','ER']]
train_stats = train_dataset1.describe()
train_stats = train_stats.transpose()
#print(train_stats)

train_labels = train_dataset.pop('wicketTaken')
test_labels = test_dataset.pop('wicketTaken')

# Create a Deep Learning model with keras
model = tf.keras.Sequential([
    tf.keras.layers.Embedding(vector_size,16,input_length=5),
    tf.keras.layers.Flatten(),
    keras.layers.Dropout(.2),
    keras.layers.Dense(16),
 
    keras.layers.Dense(8,activation=tf.nn.relu),
    
    keras.layers.Dense(4,activation=tf.nn.relu),
    keras.layers.Dense(1)
  ])

# Print the model summary
#model.summary()
# Use the Adam optimizer with a learning rate of 0.01
#optimizer=keras.optimizers.Adam(learning_rate=.0009, beta_1=0.5, beta_2=0.999, epsilon=None, decay=0.0, amsgrad=True)
#optimizer=keras.optimizers.RMSprop(learning_rate=0.01, rho=0.2, momentum=0.2, epsilon=1e-07)
#optimizer=keras.optimizers.SGD(learning_rate=.009,momentum=0.1) - Works without dropout
optimizer=keras.optimizers.SGD(learning_rate=.01,momentum=0.1)

model.compile(loss='mean_squared_error',
                optimizer=optimizer,
                )

 # Setup the training parameters
#model.compile(loss='binary_crossentropy',optimizer='rmsprop',metrics=['accuracy'])
# Create a model
history=model.fit(
  train_dataset1, train_labels,batch_size=32,
  epochs=40, validation_data = (test_dataset1,test_labels), verbose=1)

e) Plot losses

f) Predict wickets that will be taken by bowlers against random batsmen


df5= df4[['bowler','batsman','balls','runsConceded','ER']]
test1 = df5.sample(n=10)
test1.shape
for i in range(test1.shape[0]):
      print('Bowler :', index2bowlers.get(test1.iloc[i,0]), ", Batsman : ",index2batsmen.get(test1.iloc[i,1]), '- Times wicket Prediction:',model.predict(test1.iloc[[i]]))
1/1 [==============================] - 0s 90ms/step
Bowler : Harbhajan Singh , Batsman :  AM Nayar - Times wicket Prediction: [[1.0114906]]
1/1 [==============================] - 0s 18ms/step
Bowler : T Natarajan , Batsman :  Arshdeep Singh - Times wicket Prediction: [[0.98656166]]
1/1 [==============================] - 0s 19ms/step
Bowler : KK Ahmed , Batsman :  A Mishra - Times wicket Prediction: [[1.0504484]]
1/1 [==============================] - 0s 24ms/step
Bowler : M Muralitharan , Batsman :  F du Plessis - Times wicket Prediction: [[1.0941994]]
1/1 [==============================] - 0s 25ms/step
Bowler : SK Warne , Batsman :  DR Smith - Times wicket Prediction: [[1.0679393]]
1/1 [==============================] - 0s 28ms/step
Bowler : Mohammad Nabi , Batsman :  Ishan Kishan - Times wicket Prediction: [[1.403399]]
1/1 [==============================] - 0s 32ms/step
Bowler : R Bhatia , Batsman :  DJ Thornely - Times wicket Prediction: [[0.89399755]]
1/1 [==============================] - 0s 26ms/step
Bowler : SP Narine , Batsman :  MC Henriques - Times wicket Prediction: [[1.1997008]]
1/1 [==============================] - 0s 19ms/step
Bowler : AS Rajpoot , Batsman :  K Gowtham - Times wicket Prediction: [[0.9911405]]
1/1 [==============================] - 0s 21ms/step
Bowler : K Rabada , Batsman :  P Simran Singh - Times wicket Prediction: [[1.0064855]]

g) The embedding can be visualised using Google’s Embedding Projector, which identifies other batsmen who have similar characteristics. Here Cosine Similarity is used for grouping similar batsmen of IPL

The closest neighbor for AB De Villiers in IPL is SK Raina, then Rohit Sharma as seen in the visualisation below

B. Bowler Recommender T20 (BowlerRecommenderT20M1A.ipynb)

Similar to how batsman was set up,

The steps are

a) Upload data for T20 Batsman vs Bowler with Total runs scored. This will be a sparse matrix

b) Create integer dictionaries for batsman & bowler

c) Add additional features like fours, sixes and strike rate

d) Minimise loss for wicket taken

e) Display embeddings of bowlers using Tensorboard Embeddings Projector

Minimizing the loss for wicket taken using SGD

tf.random.set_seed(4)
vector_size=len(batsman2index)

#Normalize target variable
df4=df31[['bowler','batsman','totalRuns','fours','sixes','ballsFaced']]
df4['normalizedRuns'] = (df4['totalRuns'] -df4['totalRuns'].mean())/df4['totalRuns'].std()
print(df4)
train_dataset = df4.sample(frac=0.8,random_state=0)
test_dataset = df4.drop(train_dataset.index)
train_dataset1 = train_dataset[['batsman','bowler','fours','sixes','ballsFaced']]
test_dataset1 = test_dataset[['batsman','bowler','fours','sixes','ballsFaced']]

train_labels = train_dataset.pop('normalizedRuns')
test_labels = test_dataset.pop('normalizedRuns')
train_labels
print(train_dataset1)

# Create a Deep Learning model with keras
model = tf.keras.Sequential([
    tf.keras.layers.Embedding(vector_size,16,input_length=5),
    tf.keras.layers.Flatten(),
    keras.layers.Dropout(.2),
    keras.layers.Dense(16),
 
    keras.layers.Dense(8,activation=tf.nn.relu),
    
    keras.layers.Dense(4,activation=tf.nn.relu),
    keras.layers.Dense(1)
  ])

# Print the model summary
#model.summary()
# Use the Adam optimizer with a learning rate of 0.01
#optimizer=keras.optimizers.Adam(learning_rate=.0009, beta_1=0.5, beta_2=0.999, epsilon=None, decay=0.0, amsgrad=True)
#optimizer=keras.optimizers.RMSprop(learning_rate=0.001, rho=0.2, momentum=0.2, epsilon=1e-07)
#optimizer=keras.optimizers.SGD(learning_rate=.009,momentum=0.1) - Works without dropout
optimizer=keras.optimizers.SGD(learning_rate=.01,momentum=0.1)

model.compile(loss='mean_squared_error',
                optimizer=optimizer,
                )

 # Setup the training parameters
#model.compile(loss='binary_crossentropy',optimizer='rmsprop',metrics=['accuracy'])
# Create a model
history=model.fit(
  train_dataset1, train_labels,batch_size=32,
  epochs=40, validation_data = (test_dataset1,test_labels), verbose=1)
model.predict(train_dataset1[1:10])
df5= df4[['batsman','bowler','fours','sixes','ballsFaced']]
test1 = df5.sample(n=10)
model.predict(test1)
#(model.predict(test1)* df4['totalRuns'].std()) + df4['totalRuns'].mean()
for i in range(test1.shape[0]):
        print('Batsman :', index2batsman.get(test1.iloc[i,0]), ", Bowler : ",index2bowler.get(test1.iloc[i,1]), '- Total runs Prediction:',(model.predict(test1.iloc[i])* df4['totalRuns'].std()) + df4['totalRuns'].mean())
1/1 [==============================] - 0s 396ms/step
1/1 [==============================] - 0s 112ms/step
1/1 [==============================] - 0s 183ms/step
Batsman : G Chohan , Bowler :  Khawar Ali - Total runs Prediction: [[1.8883028]]
1/1 [==============================] - 0s 56ms/step
Batsman : Umar Akmal , Bowler :  LJ Wright - Total runs Prediction: [[9.305391]]
1/1 [==============================] - 0s 68ms/step
Batsman : M Shumba , Bowler :  Simi Singh - Total runs Prediction: [[19.662743]]
1/1 [==============================] - 0s 30ms/step
Batsman : CH Gayle , Bowler :  RJW Topley - Total runs Prediction: [[16.854687]]
1/1 [==============================] - 0s 39ms/step
Batsman : BA King , Bowler :  Taskin Ahmed - Total runs Prediction: [[3.5154686]]
1/1 [==============================] - 0s 102ms/step
Batsman : KD Shah , Bowler :  Avesh Khan - Total runs Prediction: [[8.411661]]
1/1 [==============================] - 0s 38ms/step
Batsman : ST Jayasuriya , Bowler :  SCJ Broad - Total runs Prediction: [[5.867449]]
1/1 [==============================] - 0s 45ms/step
Batsman : AB de Villiers , Bowler :  Saeed Ajmal - Total runs Prediction: [[15.150892]]
1/1 [==============================] - 0s 46ms/step
Batsman : SV Samson , Bowler :  J Little - Total runs Prediction: [[10.44426]]
1/1 [==============================] - 0s 102ms/step
Batsman : Zawar Farid , Bowler :  GJ Delany - Total runs Prediction: [[1.9770675]]

Identifying similar bowlers using Embeddings Projector for T20

Bhuvaneshwar Kumar’s performance is closest to CR Woakes

Note: Incidentally the accuracy in the above model was not too good. I may work on this again later!

C) Bowler Embeddings IPL – Grouping similar bowlers of IPL with Embeddings Projector (BowlerRecommenderIPLA.ipynb)

D) Batting Embeddings T20 – Grouping similar batsmen of T20 (BatsmanRecommenderT20MA.ipynb)

The Tensorboard Pmbeddings projector is also interesting. There are multiple ways the data can be visualised namely UMAP, T-SNE, PCA(included). You could play with it.

As mentioned above the Colab notebooks and data are available at Github embeddings

The ability to identify batsmen & bowlers who would perform similarly against specific bowling attacks coupled with the average runs & strike rate should give a good measure of a player’s performance.

Take a look at some of my other posts

  1. Using Reinforcement Learning to solve Gridworld
  2. Deep Learning from first principles in Python, R and Octave – Part 4
  3. Big Data 7: yorkr waltzes with Apache NiFi
  4. Programming languages in layman’s language
  5. Pitching yorkpy…swinging away from the leg stump to IPL – Part 3
  6. Re-introducing cricketr! : An R package to analyze performances of cricketers
  7. The making of Total Control Android game
  8. Presentation on “Intelligent Networks, CAMEL protocol, services & applications”
  9. Exploring Quantum Gate operations with QCSimulator

To see all posts click Index of posts

Deconstructing Convolutional Neural Networks with Tensorflow and Keras

I have been very fascinated by how Convolution Neural  Networks have been able to, so efficiently,  do image classification and image recognition CNN’s have been very successful in in both these tasks. A good paper that explores the workings of a CNN Visualizing and Understanding Convolutional Networks  by Matthew D Zeiler and Rob Fergus. They show how through a reverse process of convolution using a deconvnet.

In their paper they show how by passing the feature map through a deconvnet ,which does the reverse process of the convnet, they can reconstruct what input pattern originally caused a given activation in the feature map

In the paper they say “A deconvnet can be thought of as a convnet model that uses the same components (filtering, pooling) but in reverse, so instead of mapping pixels to features, it does the opposite. An input image is presented to the CNN and features  activation computed throughout the layers. To examine a given convnet activation, we set all other activations in the layer to zero and pass the feature maps as input to the attached deconvnet layer. Then we successively (i) unpool, (ii) rectify and (iii) filter to reconstruct the activity in the layer beneath that gave rise to the chosen activation. This is then repeated until input pixel space is reached.”

I started to scout the internet to see how I can implement this reverse process of Convolution to understand what really happens under the hood of a CNN.  There are a lot of good articles and blogs, but I found this post Applied Deep Learning – Part 4: Convolutional Neural Networks take the visualization of the CNN one step further.

This post takes VGG16 as the pre-trained network and then uses this network to display the intermediate visualizations.  While this post was very informative and also the visualizations of the various images were very clear, I wanted to simplify the problem for my own understanding.

Hence I decided to take the MNIST digit classification as my base problem. I created a simple 3 layer CNN which gives close to 99.1% accuracy and decided to see if I could do the visualization.

As mentioned in the above post, there are 3 major visualisations

  1. Feature activations at the layer
  2. Visualisation of the filters
  3. Visualisation of the class outputs

Feature Activation – This visualization the feature activation at the 3 different layers for a given input image. It can be seen that first layer  activates based on the edge of the image. Deeper layers activate in a more abstract way.

Visualization of the filters: This visualization shows what patterns the filters respond maximally to. This is implemented in Keras here

To do this the following is repeated in a loop

  • Choose a loss function that maximizes the value of a convnet filter activation
  • Do gradient ascent (maximization) in input space that increases the filter activation

Visualizing Class Outputs of the MNIST Convnet: This process is similar to determining the filter activation. Here the convnet is made to generate an image that represents the category maximally.

You can access the Google colab notebook here – Deconstructing Convolutional Neural Networks in Tensoflow and Keras

import numpy as np
import pandas as pd
import os
import tensorflow as tf
import matplotlib.pyplot as plt
from keras.layers import Dense, Dropout, Flatten
from keras.layers import Conv2D, MaxPooling2D, Input
from keras.models import Model
from sklearn.model_selection import train_test_split
from keras.utils import np_utils
Using TensorFlow backend.
In [0]:
mnist=tf.keras.datasets.mnist
# Set training and test data and labels
(training_images,training_labels),(test_images,test_labels)=mnist.load_data()
In [0]:
#Normalize training data
X =np.array(training_images).reshape(training_images.shape[0],28,28,1) 
# Normalize the images by dividing by 255.0
X = X/255.0
X.shape
# Use one hot encoding for the labels
Y = np_utils.to_categorical(training_labels, 10)
Y.shape
# Split training data into training and validation data in the ratio of 80:20
X_train, X_validation, y_train, y_validation = train_test_split(X,Y,test_size=0.20, random_state=42)
In [4]:
# Normalize test data
X_test =np.array(test_images).reshape(test_images.shape[0],28,28,1) 
X_test=X_test/255.0
#Use OHE for the test labels
Y_test = np_utils.to_categorical(test_labels, 10)
X_test.shape
Out[4]:
(10000, 28, 28, 1)

Display data

Display the training data and the corresponding labels

In [5]:
print(training_labels[0:10])
f, axes = plt.subplots(1, 10, sharey=True,figsize=(10,10))
for i,ax in enumerate(axes.flat):
    ax.axis('off')
    ax.imshow(X[i,:,:,0],cmap="gray")

Create a Convolutional Neural Network

The CNN consists of 3 layers

  • Conv2D of size 28 x 28 with 24 filters
  • Perform Max pooling
  • Conv2D of size 14 x 14 with 48 filters
  • Perform max pooling
  • Conv2d of size 7 x 7 with 64 filters
  • Flatten
  • Use Dense layer with 128 units
  • Perform 25% dropout
  • Perform categorical cross entropy with softmax activation function
In [0]:
num_classes=10
inputs = Input(shape=(28,28,1))
x = Conv2D(24,kernel_size=(3,3),padding='same',activation="relu")(inputs)
x = MaxPooling2D(pool_size=(2, 2))(x)
x = Conv2D(48, (3, 3), padding='same',activation='relu')(x)
x = MaxPooling2D(pool_size=(2, 2))(x)
x = Conv2D(64, (3, 3), padding='same',activation='relu')(x)
x = MaxPooling2D(pool_size=(2, 2))(x)
x = Flatten()(x)
x = Dense(128, activation='relu')(x)
x = Dropout(0.25)(x)
output = Dense(num_classes,activation="softmax")(x)

model = Model(inputs,output)

model.compile(loss='categorical_crossentropy', 
          optimizer='adam', 
          metrics=['accuracy'])

Summary of CNN

Display the summary of CNN

In [7]:
model.summary()
Model: "model_1"
_________________________________________________________________
Layer (type)                 Output Shape              Param #   
=================================================================
input_1 (InputLayer)         (None, 28, 28, 1)         0         
_________________________________________________________________
conv2d_1 (Conv2D)            (None, 28, 28, 24)        240       
_________________________________________________________________
max_pooling2d_1 (MaxPooling2 (None, 14, 14, 24)        0         
_________________________________________________________________
conv2d_2 (Conv2D)            (None, 14, 14, 48)        10416     
_________________________________________________________________
max_pooling2d_2 (MaxPooling2 (None, 7, 7, 48)          0         
_________________________________________________________________
conv2d_3 (Conv2D)            (None, 7, 7, 64)          27712     
_________________________________________________________________
max_pooling2d_3 (MaxPooling2 (None, 3, 3, 64)          0         
_________________________________________________________________
flatten_1 (Flatten)          (None, 576)               0         
_________________________________________________________________
dense_1 (Dense)              (None, 128)               73856     
_________________________________________________________________
dropout_1 (Dropout)          (None, 128)               0         
_________________________________________________________________
dense_2 (Dense)              (None, 10)                1290      
=================================================================
Total params: 113,514
Trainable params: 113,514
Non-trainable params: 0
_________________________________________________________________

Perform Gradient descent and validate with the validation data

In [8]:
epochs = 20
batch_size=256
history = model.fit(X_train,y_train,
         epochs=epochs,
         batch_size=batch_size,
         validation_data=(X_validation,y_validation))
————————————————
acc = history.history[ ‘accuracy’ ]
val_acc = history.history[ ‘val_accuracy’ ]
loss = history.history[ ‘loss’ ]
val_loss = history.history[‘val_loss’ ]
epochs = range(len(acc)) # Get number of epochs
#————————————————
# Plot training and validation accuracy per epoch
#————————————————
plt.plot ( epochs, acc,label=”training accuracy” )
plt.plot ( epochs, val_acc, label=’validation acuracy’ )
plt.title (‘Training and validation accuracy’)
plt.legend()
plt.figure()
#————————————————
# Plot training and validation loss per epoch
#————————————————
plt.plot ( epochs, loss , label=”training loss”)
plt.plot ( epochs, val_loss,label=”validation loss” )
plt.title (‘Training and validation loss’ )
plt.legend()
Test model on test data
f, axes = plt.subplots(1, 10, sharey=True,figsize=(10,10))
for i,ax in enumerate(axes.flat):
ax.axis(‘off’)
ax.imshow(X_test[i,:,:,0],cmap=”gray”)
l=[]
for i in range(10):
  x=X_test[i].reshape(1,28,28,1)
  y=model.predict(x)
  m = np.argmax(y, axis=1)
  print(m)
[7]
[2]
[1]
[0]
[4]
[1]
[4]
[9]
[5]
[9]

Generate the filter activations at the intermediate CNN layers

In [12]:
img = test_images[51].reshape(1,28,28,1)
fig = plt.figure(figsize=(5,5))
print(img.shape)
plt.imshow(img[0,:,:,0],cmap="gray")
plt.axis('off')

Display the activations at the intermediate layers

This displays the intermediate activations as the image passes through the filters and generates these feature maps

In [13]:
layer_names = ['conv2d_4', 'conv2d_5', 'conv2d_6']

layer_outputs = [layer.output for layer in model.layers if 'conv2d' in layer.name]
activation_model = Model(inputs=model.input,outputs=layer_outputs)
intermediate_activations = activation_model.predict(img)
images_per_row = 8
max_images = 8

for layer_name, layer_activation in zip(layer_names, intermediate_activations):
    print(layer_name,layer_activation.shape)
    n_features = layer_activation.shape[-1]
    print("features=",n_features)
    n_features = min(n_features, max_images)
    print(n_features)

    size = layer_activation.shape[1]
    print("size=",size)
    n_cols = n_features // images_per_row
    display_grid = np.zeros((size * n_cols, images_per_row * size))


    for col in range(n_cols):
      for row in range(images_per_row):
          channel_image = layer_activation[0,:, :, col * images_per_row + row]

          channel_image -= channel_image.mean()
          channel_image /= channel_image.std()
          channel_image *= 64
          channel_image += 128
          channel_image = np.clip(channel_image, 0, 255).astype('uint8')
          display_grid[col * size : (col + 1) * size,
                         row * size : (row + 1) * size] = channel_image
    scale = 2. / size
    plt.figure(figsize=(scale * display_grid.shape[1],
                        scale * display_grid.shape[0]))
    plt.axis('off')
    plt.title(layer_name)
    plt.grid(False)
    plt.imshow(display_grid, aspect='auto', cmap='viridis')
    
plt.show()

It can be seen that at the higher layers only abstract features of the input image are captured
# To fix the ImportError: cannot import name 'imresize' in the next cell. Run this cell. Then comment and restart and run all
#!pip install scipy==1.1.0

Visualize the pattern that the filters respond to maximally

  • Choose a loss function that maximizes the value of the CNN filter in a given layer
  • Start from a blank input image.
  • Do gradient ascent in input space. Modify input values so that the filter activates more
  • Repeat this in a loop.
In [14]:
from vis.visualization import visualize_activation, get_num_filters
from vis.utils import utils
from vis.input_modifiers import Jitter

max_filters = 24
selected_indices = []
vis_images = [[], [], [], [], []]
i = 0
selected_filters = [[0, 3, 11, 15, 16, 17, 18, 22], 
    [8, 21, 23, 25, 31, 32, 35, 41], 
    [2, 7, 11, 14, 19, 26, 35, 48]]

# Set the layers
layer_name = ['conv2d_4', 'conv2d_5', 'conv2d_6']
# Set the layer indices
layer_idx = [1,3,5]
for layer_name,layer_idx in zip(layer_name,layer_idx):


    # Visualize all filters in this layer.
    if selected_filters:
        filters = selected_filters[i]
    else:
        # Randomly select filters
        filters = sorted(np.random.permutation(get_num_filters(model.layers[layer_idx]))[:max_filters])
    selected_indices.append(filters)

    # Generate input image for each filter.
    # Loop through the selected filters in each layer and generate the activation of these filters
    for idx in filters:
        img = visualize_activation(model, layer_idx, filter_indices=idx, tv_weight=0., 
                                   input_modifiers=[Jitter(0.05)], max_iter=300) 
        vis_images[i].append(img)

    # Generate stitched image palette with 4 cols so we get 2 rows.
    stitched = utils.stitch_images(vis_images[i], cols=4)    
    plt.figure(figsize=(20, 30))
    plt.title(layer_name)
    plt.axis('off')
    stitched = stitched.reshape(1,61,127,1)
    plt.imshow(stitched[0,:,:,0])
    plt.show()
    i += 1
from vis.utils import utils
new_vis_images = [[], [], [], [], []]
i = 0
layer_name = ['conv2d_4', 'conv2d_5', 'conv2d_6']
layer_idx = [1,3,5]
for layer_name,layer_idx in zip(layer_name,layer_idx):
   
    # Generate input image for each filter.
    for j, idx in enumerate(selected_indices[i]):
        img = visualize_activation(model, layer_idx, filter_indices=idx, 
                                   seed_input=vis_images[i][j], input_modifiers=[Jitter(0.05)], max_iter=300) 
        #img = utils.draw_text(img, 'Filter {}'.format(idx))  
        new_vis_images[i].append(img)

    stitched = utils.stitch_images(new_vis_images[i], cols=4)   
    plt.figure(figsize=(20, 30))
    plt.title(layer_name)
    plt.axis('off')
    print(stitched.shape)
    stitched = stitched.reshape(1,61,127,1)
    plt.imshow(stitched[0,:,:,0])
    plt.show()
    i += 1

Visualizing Class Outputs

Here the CNN will generate the image that maximally represents the category. Each of the output represents one of the digits as can be seen below

In [16]:
from vis.utils import utils
from keras import activations
codes = '''
zero 0
one 1
two 2
three 3
four 4
five 5
six 6
seven 7
eight 8
nine 9
'''
layer_idx=10
initial = []
images = []
tuples = []
# Swap softmax with linear for better visualization
model.layers[layer_idx].activation = activations.linear
model = utils.apply_modifications(model)
for line in codes.split('\n'):
    if not line:
        continue
    name, idx = line.rsplit(' ', 1)
    idx = int(idx)
    img = visualize_activation(model, layer_idx, filter_indices=idx, 
                               tv_weight=0., max_iter=300, input_modifiers=[Jitter(0.05)])

    initial.append(img)
    tuples.append((name, idx))

i = 0
for name, idx in tuples:
    img = visualize_activation(model, layer_idx, filter_indices=idx,
                               seed_input = initial[i], max_iter=300, input_modifiers=[Jitter(0.05)])
    #img = utils.draw_text(img, name) # Unable to display text on gray scale image
    i += 1
    images.append(img)

stitched = utils.stitch_images(images, cols=4)
plt.figure(figsize=(20, 20))
plt.axis('off')
stitched = stitched.reshape(1,94,127,1)
plt.imshow(stitched[0,:,:,0])

plt.show()

In the grid below the class outputs show the MNIST digits to which output responds to maximally. We can see the ghostly outline
of digits 0 – 9. We can clearly see the outline if 0,1, 2,3,4,5 (yes, it is there!),6,7, 8 and 9. If you look at this from a little distance the digits are clearly visible. Isn’t that really cool!!


 

Conclusion:


It is really interesting to see the class outputs which show the image to which the class output responds to maximally. In the
post Applied Deep Learning – Part 4: Convolutional Neural Networks the class output show much more complicated images and is worth a look. It is really interesting to note that the model has adjusted the filter values and the weights of the fully connected network to maximally respond to the MNIST digits

References

1. Visualizing and Understanding Convolutional Networks
2. Applied Deep Learning – Part 4: Convolutional Neural Networks
3. Visualizing Intermediate Activations of a CNN trained on the MNIST Dataset
4. How convolutional neural networks see the world
5. Keras – Activation_maximization

Also see

1. Using Reinforcement Learning to solve Gridworld
2. Deep Learning from first principles in Python, R and Octave – Part 8
3. Cricketr learns new tricks : Performs fine-grained analysis of players
4. Video presentation on Machine Learning, Data Science, NLP and Big Data – Part 1
5. Big Data-2: Move into the big league:Graduate from R to SparkR
6. OpenCV: Fun with filters and convolution
7. Powershell GUI – Adding bells and whistles

To see all posts click Index of posts

Understanding Neural Style Transfer with Tensorflow and Keras

Neural Style Transfer (NST)  is a fascinating area of Deep Learning and Convolutional Neural Networks. NST is an interesting technique, in which the style from an image, known as the ‘style image’ is transferred to another image ‘content image’ and we get a third a image which is a generated image which has the content of the original image and the style of another image.

NST can be used to reimagine how famous painters like Van Gogh, Claude Monet or a Picasso would have visualised a scenery or architecture. NST uses Convolutional Neural Networks (CNNs) to achieve this artistic style transfer from one image to another. NST was originally implemented by Gati et al., in their paper Neural Algorithm of Artistic Style. Convolutional Neural Networks have been very successful in image classification image recognition et cetera. CNN networks have also been have also generated very interesting pictures using Neural Style Transfer which will be shown in this post. An interesting aspect of CNN’s is that the first couple of layers in the CNN capture basic features of the image like edges and  pixel values. But as we go deeper into the CNN, the network captures higher level features of the input image.

To get started with Neural Style transfer  we will be using the VGG19 pre-trained network. The VGG19 CNN is a compact pre-trained your network which can be used for performing the NST. However, we could have also used Resnet or InceptionV3 networks for this purpose but these are very large networks. The idea of using a network trained on a different task and applying it to a new task is called transfer learning.

What needs to be done to transfer the style from one of the image to another image. This brings us to the question – What is ‘style’? What is it that distinguishes Van Gogh’s painting or Picasso’s cubist art. Convolutional Neural Networks capture basic features in the lower layers and much more complex features in the deeper layers.  Style can be computed by taking the correlation of the feature maps in a layer L. This is my interpretation of how style is captured.  Since style  is intrinsic to  the image, it  implies that the style feature would exist across all the filters in a layer. Hence, to pick up this style we would need to get the correlation of the filters across channels of a lawyer. This is computed mathematically, using the Gram matrix which calculates the correlation of the activation of a the filter by the style image and generated image

To transfer the style from one image to the content image we need to do two parallel operations while doing forward propagation
– Compute the content loss between the source image and the generated image
– Compute the style loss between the style image and the generated image
– Finally we need to compute the total loss

In order to get transfer the style from the ‘style’ image to the ‘content ‘image resulting in a  ‘generated’  image  the total loss has to be minimised. Therefore backward propagation with gradient descent  is done to minimise the total loss comprising of the content and style loss.

Initially we make the Generated Image ‘G’ the same as the source image ‘S’

The content loss at layer ‘l’

L_{content} = 1/2 \sum_{i}^{j} ( F^{l}_{i,j} - P^{l}_{i,j})^{2}

where F^{l}_{i,j} and P^{l}_{i,j} represent the activations at layer ‘l’ in a filter i, at position ‘j’. The intuition is that the activations will be same for similar source and generated image. We need to minimise the content loss so that the generated stylized image is as close to the original image as possible. An intermediate layer of VGG19 block5_conv2 is used

The Style layers that are are used are

style_layers = [‘block1_conv1’,
‘block2_conv1’,
‘block3_conv1’,
‘block4_conv1’,
‘block5_conv1’]
To compute the Style Loss the Gram matrix needs to be computed. The Gram Matrix is computed by unrolling the filters as shown below (source: Convolutional Neural Networks by Prof Andrew Ng, Coursera). The result is a matrix of size n_{c} x n_{c} where n_{c} is the number of channels
The above diagram shows the filters of height n_{H} and width n_{W} with n_{C} channels
The contribution of layer ‘l’ to style loss is given by
L^{'}_{style} = \frac{\sum_{i}^{j} (G^{2}_{i,j} - A^l{i,j})^2}{4N^{2}_{l}M^{2}_{l}}
where G_{i,j}  and A_{i,j} are the Gram matrices of the style and generated images respectively. By minimising the distance in the gram matrices of the style and generated image we can ensure that generated image is a stylized version of the original image similar to the style image
The total loss is given by
L_{total} = \alpha L_{content} + \beta L_{style}
Back propagation with gradient descent works to minimise the content loss between the source and generated image, while the style loss tries to minimise the discrepancies in the style of the style image and generated image. Running through forward and backpropagation through several epochs successfully transfers the style from the style image to the source image.
You can check the Notebook at Neural Style Transfer

Note: The code in this notebook is largely based on the Neural Style Transfer tutorial from Tensorflow, though I may have taken some changes from other blogs. I also made a few changes to the code in this tutorial, like removing the scaling factor, or the class definition (Personally, I belong to the old school (C language) and am not much in love with the ‘self.”..All references are included below

Note: Here is a interesting thought. Could we do a Neural Style Transfer in music? Imagine Carlos Santana playing ‘Hotel California’ or Brian May style in ‘Another brick in the wall’. While our first reaction would be that it may not sound good as we are used to style of these songs, we may be surprised by a possible style transfer. This is definitely music to the ears!

 

Here are few runs from this

A) Run 1

1. Neural Style Transfer – a) Content Image – My portrait.  b) Style Image – Wassily Kadinsky Oil on canvas, 1913, Vassily Kadinsky’s composition

 

2. Result of Neural Style Transfer

 

 

2) Run 2

a) Content Image – Portrait of my parents b) Style Image –  Vincent Van Gogh’s ,Starry Night Oil on canvas 1889

 

2. Result of Neural Style Transfer

 

 

Run 3

1.  Content Image – Caesar 2 (Masai Mara- 20 Jun 2018).  Style Image – The Great Wave at Kanagawa – Katsushika Hokosai, 1826-1833

 

Screenshot 2020-04-12 at 12.40.44 PM

2. Result of Neural Style Transfer

lkg

 

 

Run 4

1.   Content Image – Junagarh Fort , Rajasthan   Sep 2016              b) Style Image – Le Pont Japonais by Claude Monet, Oil on canvas, 1920

 

 

2. Result of Neural Style Transfer

 

Neural Style Transfer is a very ingenious idea which shows that we can segregate the style of a painting and transfer to another image.

References

1. A Neural Algorithm of Artistic Style, Leon A. Gatys, Alexander S. Ecker, Matthias Bethge
2. Neural style transfer
3. Neural Style Transfer: Creating Art with Deep Learning using tf.keras and eager execution
4. Convolutional Neural Network, DeepLearning.AI Specialization, Prof Andrew Ng
5. Intuitive Guide to Neural Style Transfer

See also

1. Big Data-5: kNiFi-ing through cricket data with yorkpy
2. Cricketr adds team analytics to its repertoire
3. Cricpy performs granular analysis of players
4. My book ‘Deep Learning from first principles:Second Edition’ now on Amazon
5. Programming Zen and now – Some essential tips-2
6. The Anomaly
7. Practical Machine Learning with R and Python – Part 5
8. Literacy in India – A deepR dive
9. “Is it an animal? Is it an insect?” in Android

To see all posts click Index of posts

The mechanics of Convolutional Neural Networks in Tensorflow and Keras

Convolutional Neural Networks (CNNs), have been very popular in the last decade or so. CNNs have been used in multiple applications like image recognition, image classification, facial recognition, neural style transfer etc. CNN’s have been extremely successful in handling these kind of problems. How do they work? What makes them so successful? What is the principle behind CNN’s ?

Note: this post is based on two Coursera courses I did, namely namely Deep Learning specialisation by Prof Andrew Ng and Tensorflow Specialisation by  Laurence Moroney.

In this post I show you how CNN’s work. To understand how CNNs work, we need to understand the concept behind machine learning algorithms. If you take a simple machine learning algorithm in which you are trying to do multi-class classification using softmax or binary classification with the sigmoid function, for a set of for a set of input features against a target variable we need to create an objective function of the input features versus the target variable. Then we need to minimise this objective function, while performing gradient descent, such that the cost  is the lowest. This will give the set of weights for the different variables in the objective function.

The central problem in ML algorithms is to do feature selection, i.e.  we need to find the set of features that actually influence the target.  There are various methods for doing features selection – best fit, forward fit, backward fit, ridge and lasso regression. All these methods try to pick out the predictors that influence the output most, by making the weights of the other features close to zero. Please look at my post – Practical Machine Learning in R and Python – Part 3, where I show you the different methods for doing features selection.

In image classification or Image recognition we need to find the important features in the image. How do we do that? Many years back, have played around with OpenCV.  While working with OpenCV I came across are numerous filters like the Sobel ,the Laplacian, Canny, Gaussian filter et cetera which can be used to identify key features of the image. For example the Canny filter feature can be used for edge detection, Gaussian for smoothing, Sobel for determining the derivative and we have other filters for detecting vertical or horizontal edges. Take a look at my post Computer Vision: Ramblings on derivatives, histograms and contours So for handling images we need to apply these filters to pick  out the key features of the image namely the edges and other features. So rather than using the entire image’s pixels against the target class we can pick out the features from the image and use that as predictors of the target output.

Note: that in Convolutional Neural Network, fixed filter values like the those shown above  are not used directly. Rather the filter values are learned through back propagation and gradient descent as shown below.

In CNNs the filter values are considered to be weights which are then learned and updated in each forward/backward propagation cycle much like the way a fully connected Deep Learning Network learns the weights of the network.

Here is a short derivation of the most important parts of how a CNNs work

The convolution of a filter F with the input X can be represented as.

 

 

Convolving we get

 

This the forward propagation as it passes through a non-linear function like Relu

 

To go through back propagation we need to compute the \partial L  at every node of Convolutional Neural network

 

The loss with respect to the output is \partial L/\partial O. \partial O/\partial X & \partial O/\partial F are the local derivatives

We need these local derivatives because we can learn the filter values using gradient descent

where \alpha is the learning rate. Also \partial L/\partial X is the loss which is back propagated to the previous layers. You can see the detailed derivation of back propagation in my post Deep Learning from first principles in Python, R and Octave – Part 3 in a L-layer, multi-unit Deep Learning network.

In the fully connected layers the weights associated with each connection is computed in every cycle of forward and backward propagation using gradient descent. Similarly, the filter values are also computed and updated in each forward and backward propagation cycle. This is done so as to minimize the loss at the output layer.

By using the chain rule and simplifying the back propagation for the Convolutional layers we get these 2 equations. The first equation is used to learn the filter values and the second is used pass the loss to layers before

(for the detailed derivation see Convolutions and Backpropagations

An important aspect of performing convolutions is to reduce the size of  the flattened image that is passed into the fully connected DL network. Successively convolving with 2D filters and doing a max pooling helps to reduce the size of the features that we can use for learning the images. Convolutions also enable a sparsity of connections  as you can see in the diagram below. In the LeNet-5 Convolution Neural Network of Yann Le Cunn, successive convolutions reduce the image size from 28 x 28=784 to 120 flattened values.

Here is an interesting Deep Learning problem. Convolutions help in picking out important features of images and help in image classification/ detection. What would be its equivalent if we wanted to identify the Carnatic ragam of a song? A Carnatic ragam is roughly similar to Western scales (major, natural, melodic, blues) with all its modes Lydian, Aeolion, Phyrgian etc. Except in the case of the ragams, it is more nuanced, complex and involved. Personally, I can rarely identify a ragam on which a carnatic song is based (I am tone deaf when it comes to identifying ragams). I have come to understand that each Carnatic ragam has its own character, which is made up of several melodic phrases which are unique to that flavor of a ragam. What operation like convolution would be needed so that we can pick out these unique phrases in a Carnatic ragam? Of course, we would need to use it in Recurrent Neural Networks with LSTMs as a song is a time sequence of notes to identify sequences. Nevertheless, if there was some operation with which we can pick up the distinct, unique phrases from a song and then run it through a classifier, maybe we would be able to identify the ragam of the song.

Below I implement 3 simple CNN using the Dogs vs Cats Dataset from Kaggle. The first CNN uses regular Convolutions a Fully connected network to classify the images. The second approach uses Image Augmentation. For some reason, I did not get a better performance with Image Augumentation. Thirdly I use the pre-trained Inception v3 network.

 

1. Basic Convolutional Neural Network in Tensorflow & Keras

You can view the Colab notebook here – Cats_vs_dogs_1.ipynb

Here some important parts of the notebook

Create CNN Model

  • Use 3 Convolution + Max pooling layers with 32,64 and 128 filters respectively
  • Flatten the data
  • Have 2 Fully connected layers with 128, 512 neurons with relu activation
  • Use sigmoid for binary classification
In [0]:
model = tf.keras.models.Sequential([
    tf.keras.layers.Conv2D(32,(3,3),activation='relu',input_shape=(150,150,3)),
    tf.keras.layers.MaxPooling2D(2,2),
    tf.keras.layers.Conv2D(64,(3,3),activation='relu'),
    tf.keras.layers.MaxPooling2D(2,2),
    tf.keras.layers.Conv2D(128,(3,3),activation='relu'),
    tf.keras.layers.MaxPooling2D(2,2),
    tf.keras.layers.Flatten(),
    tf.keras.layers.Dense(128,activation='relu'),
    tf.keras.layers.Dense(512,activation='relu'),
    tf.keras.layers.Dense(1,activation='sigmoid')
])

Print model summary

In [13]:
model.summary()
Model: "sequential"
_________________________________________________________________
Layer (type)                 Output Shape              Param #   
=================================================================
conv2d (Conv2D)              (None, 148, 148, 32)      896       
_________________________________________________________________
max_pooling2d (MaxPooling2D) (None, 74, 74, 32)        0         
_________________________________________________________________
conv2d_1 (Conv2D)            (None, 72, 72, 64)        18496     
_________________________________________________________________
max_pooling2d_1 (MaxPooling2 (None, 36, 36, 64)        0         
_________________________________________________________________
conv2d_2 (Conv2D)            (None, 34, 34, 128)       73856     
_________________________________________________________________
max_pooling2d_2 (MaxPooling2 (None, 17, 17, 128)       0         
_________________________________________________________________
flatten (Flatten)            (None, 36992)             0         
_________________________________________________________________
dense (Dense)                (None, 128)               4735104   
_________________________________________________________________
dense_1 (Dense)              (None, 512)               66048     
_________________________________________________________________
dense_2 (Dense)              (None, 1)                 513       
=================================================================
Total params: 4,894,913
Trainable params: 4,894,913
Non-trainable params: 0
_________________________________________________________________

Use the Adam Optimizer with binary cross entropy

model.compile(optimizer='adam',
             loss='binary_crossentropy',
             metrics=['accuracy'])

Perform Gradient Descent

  • Do Gradient Descent for 15 epochs
history=model.fit(train_generator,
                 validation_data=validation_generator,
                 steps_per_epoch=100,
                 epochs=15,
                 validation_steps=50,
                 verbose=2)
Epoch 1/15
100/100 - 13s - loss: 0.6821 - accuracy: 0.5425 - val_loss: 0.6484 - val_accuracy: 0.6131
Epoch 2/15
100/100 - 13s - loss: 0.6227 - accuracy: 0.6456 - val_loss: 0.6161 - val_accuracy: 0.6394
Epoch 3/15
100/100 - 13s - loss: 0.5975 - accuracy: 0.6719 - val_loss: 0.5558 - val_accuracy: 0.7206
Epoch 4/15
100/100 - 13s - loss: 0.5480 - accuracy: 0.7241 - val_loss: 0.5431 - val_accuracy: 0.7138
Epoch 5/15
100/100 - 13s - loss: 0.5182 - accuracy: 0.7447 - val_loss: 0.4839 - val_accuracy: 0.7606
Epoch 6/15
100/100 - 13s - loss: 0.4773 - accuracy: 0.7781 - val_loss: 0.5029 - val_accuracy: 0.7506
Epoch 7/15
100/100 - 13s - loss: 0.4466 - accuracy: 0.7972 - val_loss: 0.4573 - val_accuracy: 0.7912
Epoch 8/15
100/100 - 13s - loss: 0.4395 - accuracy: 0.7997 - val_loss: 0.4252 - val_accuracy: 0.8119
Epoch 9/15
100/100 - 13s - loss: 0.4314 - accuracy: 0.8019 - val_loss: 0.4931 - val_accuracy: 0.7481
Epoch 10/15
100/100 - 13s - loss: 0.4309 - accuracy: 0.7969 - val_loss: 0.4203 - val_accuracy: 0.8109
Epoch 11/15
100/100 - 13s - loss: 0.4329 - accuracy: 0.7916 - val_loss: 0.4189 - val_accuracy: 0.8069
Epoch 12/15
100/100 - 13s - loss: 0.4248 - accuracy: 0.8050 - val_loss: 0.4476 - val_accuracy: 0.7925
Epoch 13/15
100/100 - 13s - loss: 0.3868 - accuracy: 0.8306 - val_loss: 0.3900 - val_accuracy: 0.8236
Epoch 14/15
100/100 - 13s - loss: 0.3710 - accuracy: 0.8328 - val_loss: 0.4520 - val_accuracy: 0.7900
Epoch 15/15
100/100 - 13s - loss: 0.3654 - accuracy: 0.8353 - val_loss: 0.3999 - val_accuracy: 0.8100

 

 

 

 

 

 

Plot results

    • Plot training and validation accuracy

 

  • Plot training and validation loss

 

 

 

 

 

 

#-----------------------------------------------------------
# Retrieve a list of list results on training and test data
# sets for each training epoch
#-----------------------------------------------------------
acc      = history.history[     'accuracy' ]
val_acc  = history.history[ 'val_accuracy' ]
loss     = history.history[    'loss' ]
val_loss = history.history['val_loss' ]

epochs   = range(len(acc)) # Get number of epochs

#------------------------------------------------
# Plot training and validation accuracy per epoch
#------------------------------------------------
plt.plot  ( epochs,     acc,label="training accuracy" )
plt.plot  ( epochs, val_acc, label='validation acuracy' )
plt.title ('Training and validation accuracy')
plt.legend()

plt.figure()

#------------------------------------------------
# Plot training and validation loss per epoch
#------------------------------------------------
plt.plot  ( epochs,     loss , label="training loss")
plt.plot  ( epochs, val_loss,label="validation loss" )
plt.title ('Training and validation loss'   )
plt.legend()



 

2. CNN with Image Augmentation

You can check the Cats_vs_Dogs_2.ipynb

Including the important parts of this implementation below

Use Image Augumentation

Use Image Augumentation to improve performance

  • Use the same model parameters as before
  • Perform the following image augmentation
    • width, height shift
    • shear and zoom

    Note: Adding rotation made the performance worse

import tensorflow as tf
from tensorflow import keras
from tensorflow.keras.optimizers import RMSprop
from tensorflow.keras.preprocessing.image import ImageDataGenerator
model = tf.keras.models.Sequential([
    tf.keras.layers.Conv2D(32,(3,3),activation='relu',input_shape=(150,150,3)),
    tf.keras.layers.MaxPooling2D(2,2),
    tf.keras.layers.Conv2D(64,(3,3),activation='relu'),
    tf.keras.layers.MaxPooling2D(2,2),
    tf.keras.layers.Conv2D(128,(3,3),activation='relu'),
    tf.keras.layers.MaxPooling2D(2,2),
    tf.keras.layers.Flatten(),
    tf.keras.layers.Dense(128,activation='relu'),
    tf.keras.layers.Dense(512,activation='relu'),
    tf.keras.layers.Dense(1,activation='sigmoid')
])


train_datagen = ImageDataGenerator(
      rescale=1./255,
      #rotation_range=90,
      width_shift_range=0.2,
      height_shift_range=0.2,
      shear_range=0.2,
      zoom_range=0.2)
      #horizontal_flip=True,
      #fill_mode='nearest')

validation_datagen = ImageDataGenerator(rescale=1./255)
#
train_generator = train_datagen.flow_from_directory(train_dir,
                                                    batch_size=32,
                                                    class_mode='binary',
                                                    target_size=(150, 150))     
# --------------------
# Flow validation images in batches of 20 using test_datagen generator
# --------------------
validation_generator =  validation_datagen.flow_from_directory(validation_dir,
                                                         batch_size=32,
                                                         class_mode  = 'binary',
                                                         target_size = (150, 150))

# Use Adam Optmizer 
model.compile(optimizer='adam',
             loss='binary_crossentropy',
             metrics=['accuracy'])
Found 20000 images belonging to 2 classes.
Found 5000 images belonging to 2 classes.

Perform Gradient Descent

history=model.fit(train_generator,
                 validation_data=validation_generator,
                 steps_per_epoch=100,
                 epochs=15,
                 validation_steps=50,
                 verbose=2)
Epoch 1/15
100/100 - 27s - loss: 0.5716 - accuracy: 0.6922 - val_loss: 0.4843 - val_accuracy: 0.7744
Epoch 2/15
100/100 - 27s - loss: 0.5575 - accuracy: 0.7084 - val_loss: 0.4683 - val_accuracy: 0.7750
Epoch 3/15
100/100 - 26s - loss: 0.5452 - accuracy: 0.7228 - val_loss: 0.4856 - val_accuracy: 0.7665
Epoch 4/15
100/100 - 27s - loss: 0.5294 - accuracy: 0.7347 - val_loss: 0.4654 - val_accuracy: 0.7812
Epoch 5/15
100/100 - 27s - loss: 0.5352 - accuracy: 0.7350 - val_loss: 0.4557 - val_accuracy: 0.7981
Epoch 6/15
100/100 - 26s - loss: 0.5136 - accuracy: 0.7453 - val_loss: 0.4964 - val_accuracy: 0.7621
Epoch 7/15
100/100 - 27s - loss: 0.5249 - accuracy: 0.7334 - val_loss: 0.4959 - val_accuracy: 0.7556
Epoch 8/15
100/100 - 26s - loss: 0.5035 - accuracy: 0.7497 - val_loss: 0.4555 - val_accuracy: 0.7969
Epoch 9/15
100/100 - 26s - loss: 0.5024 - accuracy: 0.7487 - val_loss: 0.4675 - val_accuracy: 0.7728
Epoch 10/15
100/100 - 27s - loss: 0.5015 - accuracy: 0.7500 - val_loss: 0.4276 - val_accuracy: 0.8075
Epoch 11/15
100/100 - 26s - loss: 0.5002 - accuracy: 0.7581 - val_loss: 0.4193 - val_accuracy: 0.8131
Epoch 12/15
100/100 - 27s - loss: 0.4733 - accuracy: 0.7706 - val_loss: 0.5209 - val_accuracy: 0.7398
Epoch 13/15
100/100 - 27s - loss: 0.4999 - accuracy: 0.7538 - val_loss: 0.4109 - val_accuracy: 0.8075
Epoch 14/15
100/100 - 27s - loss: 0.4550 - accuracy: 0.7859 - val_loss: 0.3770 - val_accuracy: 0.8288
Epoch 15/15
100/100 - 26s - loss: 0.4688 - accuracy: 0.7688 - val_loss: 0.4764 - val_accuracy: 0.7786

Plot results

  • Plot training and validation accuracy
  • Plot training and validation loss
In [15]:
import matplotlib.pyplot as plt
#-----------------------------------------------------------
# Retrieve a list of list results on training and test data
# sets for each training epoch
#-----------------------------------------------------------
acc      = history.history[     'accuracy' ]
val_acc  = history.history[ 'val_accuracy' ]
loss     = history.history[    'loss' ]
val_loss = history.history['val_loss' ]

epochs   = range(len(acc)) # Get number of epochs

#------------------------------------------------
# Plot training and validation accuracy per epoch
#------------------------------------------------
plt.plot  ( epochs,     acc,label="training accuracy" )
plt.plot  ( epochs, val_acc, label='validation acuracy' )
plt.title ('Training and validation accuracy')
plt.legend()

plt.figure()

#------------------------------------------------
# Plot training and validation loss per epoch
#------------------------------------------------
plt.plot  ( epochs,     loss , label="training loss")
plt.plot  ( epochs, val_loss,label="validation loss" )
plt.title ('Training and validation loss'   )
plt.legend()
 


Implementation using Inception Network V3

The implementation is in the Colab notebook Cats_vs_Dog_3.ipynb

This is implemented as below

Use Inception V3

import os

from tensorflow.keras import layers
from tensorflow.keras import Model

  
from tensorflow.keras.applications.inception_v3 import InceptionV3
pre_trained_model = InceptionV3(input_shape = (150, 150, 3), 
                                include_top = False, 
                                weights = 'imagenet')


for layer in pre_trained_model.layers:
  layer.trainable = False
  
# pre_trained_model.summary()

last_layer = pre_trained_model.get_layer('mixed7')
print('last layer output shape: ', last_layer.output_shape)
last_output = last_layer.output
Downloading data from https://storage.googleapis.com/tensorflow/keras-applications/inception_v3/inception_v3_weights_tf_dim_ordering_tf_kernels_notop.h5
87916544/87910968 [==============================] - 1s 0us/step
last layer output shape:  (None, 7, 7, 768)

Use Layer 7 of Inception Network

  • Use Image Augumentation
  • Use Adam Optimizer
In [0]:
import tensorflow as tf
from tensorflow import keras
from tensorflow.keras.optimizers import RMSprop
from tensorflow.keras.preprocessing.image import ImageDataGenerator
# Flatten the output layer to 1 dimension
x = layers.Flatten()(last_output)
# Add a fully connected layer with 1,024 hidden units and ReLU activation
x = layers.Dense(1024, activation='relu')(x)
# Add a dropout rate of 0.2
x = layers.Dropout(0.2)(x)                  
# Add a final sigmoid layer for classification
x = layers.Dense  (1, activation='sigmoid')(x)           

model = Model( pre_trained_model.input, x) 
#train_datagen = ImageDataGenerator( rescale = 1.0/255. )
#validation_datagen = ImageDataGenerator( rescale = 1.0/255. )

train_datagen = ImageDataGenerator(
      rescale=1./255,
      #rotation_range=90,
      width_shift_range=0.2,
      height_shift_range=0.2,
      shear_range=0.2,
      zoom_range=0.2)
      #horizontal_flip=True,
      #fill_mode='nearest')

validation_datagen = ImageDataGenerator(rescale=1./255)
#
train_generator = train_datagen.flow_from_directory(train_dir,
                                                    batch_size=32,
                                                    class_mode='binary',
                                                    target_size=(150, 150))     
# --------------------
# Flow validation images in batches of 20 using test_datagen generator
# --------------------
validation_generator =  validation_datagen.flow_from_directory(validation_dir,
                                                         batch_size=32,
                                                         class_mode  = 'binary',
                                                         target_size = (150, 150))


model.compile(optimizer='adam',
             loss='binary_crossentropy',
             metrics=['accuracy'])
Found 20000 images belonging to 2 classes.
Found 5000 images belonging to 2 classes.

Fit model

history=model.fit(train_generator,
                 validation_data=validation_generator,
                 steps_per_epoch=100,
                 epochs=15,
                 validation_steps=50,
                 verbose=2)
Epoch 1/15
100/100 - 31s - loss: 0.5961 - accuracy: 0.8909 - val_loss: 0.1919 - val_accuracy: 0.9456
Epoch 2/15
100/100 - 30s - loss: 0.2002 - accuracy: 0.9259 - val_loss: 0.1025 - val_accuracy: 0.9550
Epoch 3/15
100/100 - 30s - loss: 0.1618 - accuracy: 0.9366 - val_loss: 0.0920 - val_accuracy: 0.9581
Epoch 4/15
100/100 - 29s - loss: 0.1442 - accuracy: 0.9381 - val_loss: 0.0960 - val_accuracy: 0.9600
Epoch 5/15
100/100 - 30s - loss: 0.1402 - accuracy: 0.9381 - val_loss: 0.0703 - val_accuracy: 0.9794
Epoch 6/15
100/100 - 30s - loss: 0.1437 - accuracy: 0.9413 - val_loss: 0.1090 - val_accuracy: 0.9531
Epoch 7/15
100/100 - 30s - loss: 0.1325 - accuracy: 0.9428 - val_loss: 0.0756 - val_accuracy: 0.9670
Epoch 8/15
100/100 - 29s - loss: 0.1341 - accuracy: 0.9491 - val_loss: 0.0625 - val_accuracy: 0.9737
Epoch 9/15
100/100 - 29s - loss: 0.1186 - accuracy: 0.9513 - val_loss: 0.0934 - val_accuracy: 0.9581
Epoch 10/15
100/100 - 29s - loss: 0.1171 - accuracy: 0.9513 - val_loss: 0.0642 - val_accuracy: 0.9727
Epoch 11/15
100/100 - 29s - loss: 0.1018 - accuracy: 0.9591 - val_loss: 0.0930 - val_accuracy: 0.9606
Epoch 12/15
100/100 - 29s - loss: 0.1190 - accuracy: 0.9541 - val_loss: 0.0737 - val_accuracy: 0.9719
Epoch 13/15
100/100 - 29s - loss: 0.1223 - accuracy: 0.9494 - val_loss: 0.0740 - val_accuracy: 0.9695
Epoch 14/15
100/100 - 29s - loss: 0.1158 - accuracy: 0.9516 - val_loss: 0.0659 - val_accuracy: 0.9744
Epoch 15/15
100/100 - 29s - loss: 0.1168 - accuracy: 0.9591 - val_loss: 0.0788 - val_accuracy: 0.9669

Plot results

  • Plot training and validation accuracy
  • Plot training and validation loss
In [14]:
import matplotlib.pyplot as plt
#-----------------------------------------------------------
# Retrieve a list of list results on training and test data
# sets for each training epoch
#-----------------------------------------------------------
acc      = history.history[     'accuracy' ]
val_acc  = history.history[ 'val_accuracy' ]
loss     = history.history[    'loss' ]
val_loss = history.history['val_loss' ]

epochs   = range(len(acc)) # Get number of epochs

#------------------------------------------------
# Plot training and validation accuracy per epoch
#------------------------------------------------
plt.plot  ( epochs,     acc,label="training accuracy" )
plt.plot  ( epochs, val_acc, label='validation acuracy' )
plt.title ('Training and validation accuracy')
plt.legend()

plt.figure()

#------------------------------------------------
# Plot training and validation loss per epoch
#------------------------------------------------
plt.plot  ( epochs,     loss , label="training loss")
plt.plot  ( epochs, val_loss,label="validation loss" )
plt.title ('Training and validation loss'   )
plt.legend()

 

I intend to do some interesting stuff with Convolutional Neural Networks.

Watch this space!

See also
1. Architecting a cloud based IP Multimedia System (IMS)
2. Exploring Quantum Gate operations with QCSimulator
3. Big Data 6: The T20 Dance of Apache NiFi and yorkpy
4. The Many Faces of Latency
5. The Clash of the Titans in Test and ODI cricket

To see all posts click Index of posts

Getting started with Tensorflow, Keras in Python and R

The Pale Blue Dot

“From this distant vantage point, the Earth might not seem of any particular interest. But for us, it’s different. Consider again that dot. That’s here, that’s home, that’s us. On it everyone you love, everyone you know, everyone you ever heard of, every human being who ever was, lived out their lives. The aggregate of our joy and suffering, thousands of confident religions, ideologies, and economic doctrines, every hunter and forager, every hero and coward, every creator and destroyer of civilization, every king and peasant, every young couple in love, every mother and father, hopeful child, inventor and explorer, every teacher of morals, every corrupt politician, every “superstar,” every “supreme leader,” every saint and sinner in the history of our species lived there—on the mote of dust suspended in a sunbeam.”

Carl Sagan

Tensorflow and Keras are Deep Learning frameworks that really simplify a lot of things to the user. If you are familiar with Machine Learning and Deep Learning concepts then Tensorflow and Keras are really a playground to realize your ideas.  In this post I show how you can get started with Tensorflow in both Python and R

 

Tensorflow in Python

For tensorflow in Python, I found Google’s Colab an ideal environment for running your Deep Learning code. This is an Google’s research project  where you can execute your code  on GPUs, TPUs etc

Tensorflow in R (RStudio)

To execute tensorflow in R (RStudio) you need to install tensorflow and keras as shown below
In this post I show how to get started with Tensorflow and Keras in R.

# Install Tensorflow in RStudio
#install_tensorflow()
# Install Keras
#install_packages("keras")
library(tensorflow)
libary(keras)

This post takes 3 different Machine Learning problems and uses the
Tensorflow/Keras framework to solve it

Note:
You can view the Google Colab notebook at Tensorflow in Python
The RMarkdown file has been published at RPubs and can be accessed
at Getting started with Tensorflow in R

Checkout my book ‘Deep Learning from first principles: Second Edition – In vectorized Python, R and Octave’. My book starts with the implementation of a simple 2-layer Neural Network and works its way to a generic L-Layer Deep Learning Network, with all the bells and whistles. The derivations have been discussed in detail. The code has been extensively commented and included in its entirety in the Appendix sections. My book is available on Amazon as paperback ($14.99) and in kindle version($9.99/Rs449).

1. Multivariate regression with Tensorflow – Python

This code performs multivariate regression using Tensorflow and keras on the advent of Parkinson disease through sound recordings see Parkinson Speech Dataset with Multiple Types of Sound Recordings Data Set . The clinician’s motorUPDRS score has to be predicted from the set of features

In [0]:
# Import tensorflow
import tensorflow as tf
from tensorflow import keras
In [2]:
#Get the data rom the UCI Machine Learning repository
dataset = keras.utils.get_file("parkinsons_updrs.data", "https://archive.ics.uci.edu/ml/machine-learning-databases/parkinsons/telemonitoring/parkinsons_updrs.data")
Downloading data from https://archive.ics.uci.edu/ml/machine-learning-databases/parkinsons/telemonitoring/parkinsons_updrs.data
917504/911261 [==============================] - 0s 0us/step
In [3]:
# Read the CSV file 
import pandas as pd
parkinsons = pd.read_csv(dataset, na_values = "?", comment='\t',
                      sep=",", skipinitialspace=True)
print(parkinsons.shape)
print(parkinsons.columns)
#Check if there are any NAs in the rows
parkinsons.isna().sum()
(5875, 22)
Index(['subject#', 'age', 'sex', 'test_time', 'motor_UPDRS', 'total_UPDRS',
       'Jitter(%)', 'Jitter(Abs)', 'Jitter:RAP', 'Jitter:PPQ5', 'Jitter:DDP',
       'Shimmer', 'Shimmer(dB)', 'Shimmer:APQ3', 'Shimmer:APQ5',
       'Shimmer:APQ11', 'Shimmer:DDA', 'NHR', 'HNR', 'RPDE', 'DFA', 'PPE'],
      dtype='object')
Out[3]:
subject#         0
age              0
sex              0
test_time        0
motor_UPDRS      0
total_UPDRS      0
Jitter(%)        0
Jitter(Abs)      0
Jitter:RAP       0
Jitter:PPQ5      0
Jitter:DDP       0
Shimmer          0
Shimmer(dB)      0
Shimmer:APQ3     0
Shimmer:APQ5     0
Shimmer:APQ11    0
Shimmer:DDA      0
NHR              0
HNR              0
RPDE             0
DFA              0
PPE              0
dtype: int64
Note: To see how to create dummy variables see my post Practical Machine Learning with R and Python – Part 2
In [4]:
# Drop the columns subject number as it is not relevant
parkinsons1=parkinsons.drop(['subject#'],axis=1)

# Create dummy variables for sex (M/F)
parkinsons2=pd.get_dummies(parkinsons1,columns=['sex'])
parkinsons2.head()

Out[4]
age test_time motor_UPDRS total_UPDRS Jitter(%) Jitter(Abs) Jitter:RAP Jitter:PPQ5 Jitter:DDP Shimmer Shimmer(dB) Shimmer:APQ3 Shimmer:APQ5 Shimmer:APQ11 Shimmer:DDA NHR HNR RPDE DFA PPE sex_0 sex_1
0 72 5.6431 28.199 34.398 0.00662 0.000034 0.00401 0.00317 0.01204 0.02565 0.230 0.01438 0.01309 0.01662 0.04314 0.014290 21.640 0.41888 0.54842 0.16006 1 0
1 72 12.6660 28.447 34.894 0.00300 0.000017 0.00132 0.00150 0.00395 0.02024 0.179 0.00994 0.01072 0.01689 0.02982 0.011112 27.183 0.43493 0.56477 0.10810 1 0
2 72 19.6810 28.695 35.389 0.00481 0.000025 0.00205 0.00208 0.00616 0.01675 0.181 0.00734 0.00844 0.01458 0.02202 0.020220 23.047 0.46222 0.54405 0.21014 1 0
3 72 25.6470 28.905 35.810 0.00528 0.000027 0.00191 0.00264 0.00573 0.02309 0.327 0.01106 0.01265 0.01963 0.03317 0.027837 24.445 0.48730 0.57794 0.33277 1 0
4 72 33.6420 29.187 36.375 0.00335 0.000020 0.00093 0.00130 0.00278 0.01703 0.176 0.00679 0.00929 0.01819 0.02036 0.011625 26.126 0.47188 0.56122 0.19361 1 0

# Create a training and test data set with 80%/20%
train_dataset = parkinsons2.sample(frac=0.8,random_state=0)
test_dataset = parkinsons2.drop(train_dataset.index)

# Select columns
train_dataset1= train_dataset[['age', 'test_time', 'Jitter(%)', 'Jitter(Abs)',
       'Jitter:RAP', 'Jitter:PPQ5', 'Jitter:DDP', 'Shimmer', 'Shimmer(dB)',
       'Shimmer:APQ3', 'Shimmer:APQ5', 'Shimmer:APQ11', 'Shimmer:DDA', 'NHR',
       'HNR', 'RPDE', 'DFA', 'PPE', 'sex_0', 'sex_1']]
test_dataset1= test_dataset[['age','test_time', 'Jitter(%)', 'Jitter(Abs)',
       'Jitter:RAP', 'Jitter:PPQ5', 'Jitter:DDP', 'Shimmer', 'Shimmer(dB)',
       'Shimmer:APQ3', 'Shimmer:APQ5', 'Shimmer:APQ11', 'Shimmer:DDA', 'NHR',
       'HNR', 'RPDE', 'DFA', 'PPE', 'sex_0', 'sex_1']]
In [7]:
# Generate the statistics of the columns for use in normalization of the data
train_stats = train_dataset1.describe()
train_stats = train_stats.transpose()
train_stats
Out[7]:
count mean std min 25% 50% 75% max
age 4700.0 64.792766 8.870401 36.000000 58.000000 65.000000 72.000000 85.000000
test_time 4700.0 93.399490 53.630411 -4.262500 46.852250 93.405000 139.367500 215.490000
Jitter(%) 4700.0 0.006136 0.005612 0.000830 0.003560 0.004900 0.006770 0.099990
Jitter(Abs) 4700.0 0.000044 0.000036 0.000002 0.000022 0.000034 0.000053 0.000396
Jitter:RAP 4700.0 0.002969 0.003089 0.000330 0.001570 0.002235 0.003260 0.057540
Jitter:PPQ5 4700.0 0.003271 0.003760 0.000430 0.001810 0.002480 0.003460 0.069560
Jitter:DDP 4700.0 0.008908 0.009267 0.000980 0.004710 0.006705 0.009790 0.172630
Shimmer 4700.0 0.033992 0.025922 0.003060 0.019020 0.027385 0.039810 0.268630
Shimmer(dB) 4700.0 0.310487 0.231016 0.026000 0.175000 0.251000 0.363250 2.107000
Shimmer:APQ3 4700.0 0.017125 0.013275 0.001610 0.009190 0.013615 0.020562 0.162670
Shimmer:APQ5 4700.0 0.020151 0.016848 0.001940 0.010750 0.015785 0.023733 0.167020
Shimmer:APQ11 4700.0 0.027508 0.020270 0.002490 0.015630 0.022685 0.032713 0.275460
Shimmer:DDA 4700.0 0.051375 0.039826 0.004840 0.027567 0.040845 0.061683 0.488020
NHR 4700.0 0.032116 0.060206 0.000304 0.010827 0.018403 0.031452 0.748260
HNR 4700.0 21.704631 4.288853 1.659000 19.447750 21.973000 24.445250 37.187000
RPDE 4700.0 0.542549 0.100212 0.151020 0.471235 0.543490 0.614335 0.966080
DFA 4700.0 0.653015 0.070446 0.514040 0.596470 0.643285 0.710618 0.865600
PPE 4700.0 0.219559 0.091506 0.021983 0.156470 0.205340 0.264017 0.731730
sex_0 4700.0 0.681489 0.465948 0.000000 0.000000 1.000000 1.000000 1.000000
sex_1 4700.0 0.318511 0.465948 0.000000 0.000000 0.000000 1.000000 1.000000
In [0]:
# Create the target variable
train_labels = train_dataset.pop('motor_UPDRS')
test_labels = test_dataset.pop('motor_UPDRS')
In [0]:
# Normalize the data by subtracting the mean and dividing by the standard deviation
def normalize(x):
  return (x - train_stats['mean']) / train_stats['std']

# Create normalized training and test data
normalized_train_data = normalize(train_dataset1)
normalized_test_data = normalize(test_dataset1)
In [0]:
# Create a Deep Learning model with keras
model = tf.keras.Sequential([
    keras.layers.Dense(6, activation=tf.nn.relu, input_shape=[len(train_dataset1.keys())]),
    keras.layers.Dense(9, activation=tf.nn.relu),
    keras.layers.Dense(6,activation=tf.nn.relu),
    keras.layers.Dense(1)
  ])

# Use the Adam optimizer with a learning rate of 0.01
optimizer=keras.optimizers.Adam(lr=.01, beta_1=0.9, beta_2=0.999, epsilon=None, decay=0.0, amsgrad=False)

# Set the metrics required to be Mean Absolute Error and Mean Squared Error.For regression, the loss is mean_squared_error
model.compile(loss='mean_squared_error',
                optimizer=optimizer,
                metrics=['mean_absolute_error', 'mean_squared_error'])
In [0]:
# Create a model
history=model.fit(
  normalized_train_data, train_labels,
  epochs=1000, validation_data = (normalized_test_data,test_labels), verbose=0)
In [26]:
hist = pd.DataFrame(history.history)
hist['epoch'] = history.epoch
hist.tail()
Out[26]:
loss mean_absolute_error mean_squared_error val_loss val_mean_absolute_error val_mean_squared_error epoch
995 15.773989 2.936990 15.773988 16.980803 3.028168 16.980803 995
996 15.238623 2.873420 15.238622 17.458752 3.101033 17.458752 996
997 15.437594 2.895500 15.437593 16.926016 2.971508 16.926018 997
998 15.867891 2.943521 15.867892 16.950249 2.985036 16.950249 998
999 15.846878 2.938914 15.846880 17.095623 3.014504 17.095625 999
In [30]:
def plot_history(history):
  hist = pd.DataFrame(history.history)
  hist['epoch'] = history.epoch

  plt.figure()
  plt.xlabel('Epoch')
  plt.ylabel('Mean Abs Error')
  plt.plot(hist['epoch'], hist['mean_absolute_error'],
           label='Train Error')
  plt.plot(hist['epoch'], hist['val_mean_absolute_error'],
           label = 'Val Error')
  plt.ylim([2,5])
  plt.legend()

  plt.figure()
  plt.xlabel('Epoch')
  plt.ylabel('Mean Square Error ')
  plt.plot(hist['epoch'], hist['mean_squared_error'],
           label='Train Error')
  plt.plot(hist['epoch'], hist['val_mean_squared_error'],
           label = 'Val Error')
  plt.ylim([10,40])
  plt.legend()
  plt.show()


plot_history(history)

Observation

It can be seen that the mean absolute error is on an average about +/- 4.0. The validation error also is about the same. This can be reduced by playing around with the hyperparamaters and increasing the number of iterations

1a. Multivariate Regression in Tensorflow – R

# Install Tensorflow in RStudio
#install_tensorflow()
# Install Keras
#install_packages("keras")
library(tensorflow)
library(keras)
library(dplyr)
library(dummies)
## dummies-1.5.6 provided by Decision Patterns
library(tensorflow)
library(keras)

Multivariate regression

This code performs multivariate regression using Tensorflow and keras on the advent of Parkinson disease through sound recordings see Parkinson Speech Dataset with Multiple Types of Sound Recordings Data Set. The clinician’s motorUPDRS score has to be predicted from the set of features.

Read the data

# Download the Parkinson's data from UCI Machine Learning repository
dataset <- read.csv("https://archive.ics.uci.edu/ml/machine-learning-databases/parkinsons/telemonitoring/parkinsons_updrs.data")

# Set the column names
names(dataset) <- c("subject","age", "sex", "test_time","motor_UPDRS","total_UPDRS","Jitter","Jitter.Abs",
                 "Jitter.RAP","Jitter.PPQ5","Jitter.DDP","Shimmer", "Shimmer.dB", "Shimmer.APQ3",
                 "Shimmer.APQ5","Shimmer.APQ11","Shimmer.DDA", "NHR","HNR", "RPDE", "DFA","PPE")

# Remove the column 'subject' as it is not relevant to analysis
dataset1 <- subset(dataset, select = -c(subject))

# Make the column 'sex' as a factor for using dummies
dataset1$sex=as.factor(dataset1$sex)
# Add dummy variables for categorical cariable 'sex'
dataset2 <- dummy.data.frame(dataset1, sep = ".")
## Warning in model.matrix.default(~x - 1, model.frame(~x - 1), contrasts =
## FALSE): non-list contrasts argument ignored
dataset3 <- na.omit(dataset2)

Split the data as training and test in 80/20

## Split data 80% training and 20% test
sample_size <- floor(0.8 * nrow(dataset3))

## set the seed to make your partition reproducible
set.seed(12)
train_index <- sample(seq_len(nrow(dataset3)), size = sample_size)

train_dataset <- dataset3[train_index, ]
test_dataset <- dataset3[-train_index, ]

train_data <- train_dataset %>% select(sex.0,sex.1,age, test_time,Jitter,Jitter.Abs,Jitter.PPQ5,Jitter.DDP,
                              Shimmer, Shimmer.dB,Shimmer.APQ3,Shimmer.APQ11,
                              Shimmer.DDA,NHR,HNR,RPDE,DFA,PPE)

train_labels <- select(train_dataset,motor_UPDRS)
test_data <- test_dataset %>% select(sex.0,sex.1,age, test_time,Jitter,Jitter.Abs,Jitter.PPQ5,Jitter.DDP,
                              Shimmer, Shimmer.dB,Shimmer.APQ3,Shimmer.APQ11,
                              Shimmer.DDA,NHR,HNR,RPDE,DFA,PPE)
test_labels <- select(test_dataset,motor_UPDRS)

Normalize the data

 # Normalize the data by subtracting the mean and dividing by the standard deviation
normalize<-function(x) {
  y<-(x - mean(x)) / sd(x)
  return(y)
}

normalized_train_data <-apply(train_data,2,normalize)
# Convert to matrix
train_labels <- as.matrix(train_labels)
normalized_test_data <- apply(test_data,2,normalize)
test_labels <- as.matrix(test_labels)

Create the Deep Learning Model

model <- keras_model_sequential()
model %>% 
  layer_dense(units = 6, activation = 'relu', input_shape = dim(normalized_train_data)[2]) %>% 
  layer_dense(units = 9, activation = 'relu') %>%
  layer_dense(units = 6, activation = 'relu') %>%
  layer_dense(units = 1)

# Set the metrics required to be Mean Absolute Error and Mean Squared Error.For regression, the loss is 
# mean_squared_error
model %>% compile(
  loss = 'mean_squared_error',
  optimizer = optimizer_rmsprop(),
  metrics = c('mean_absolute_error','mean_squared_error')
)

# Fit the model
# Use the test data for validation
history <- model %>% fit(
  normalized_train_data, train_labels, 
  epochs = 30, batch_size = 128, 
  validation_data = list(normalized_test_data,test_labels)
)

Plot mean squared error, mean absolute error and loss for training data and test data

plot(history)

Fig1

2. Binary classification in Tensorflow – Python

This is a simple binary classification problem from UCI Machine Learning repository and deals with data on Breast cancer from the Univ. of Wisconsin Breast Cancer Wisconsin (Diagnostic) Data Set bold text

In [31]:
import tensorflow as tf
from tensorflow import keras
import pandas as pd
# Read the data set from UCI ML site
dataset_path = keras.utils.get_file("breast-cancer-wisconsin.data", "https://archive.ics.uci.edu/ml/machine-learning-databases/breast-cancer-wisconsin/breast-cancer-wisconsin.data")
raw_dataset = pd.read_csv(dataset_path, sep=",", na_values = "?", skipinitialspace=True,)
dataset = raw_dataset.copy()

#Check for Null and drop
dataset.isna().sum()
dataset = dataset.dropna()
dataset.isna().sum()

# Set the column names
dataset.columns = ["id","thickness",	"cellsize",	"cellshape","adhesion","epicellsize",
                    "barenuclei","chromatin","normalnucleoli","mitoses","class"]
dataset.head()
Downloading data from https://archive.ics.uci.edu/ml/machine-learning-databases/breast-cancer-wisconsin/breast-cancer-wisconsin.data
24576/19889 [=====================================] - 0s 1us/step
id	thickness	cellsize	cellshape	adhesion	epicellsize	barenuclei	chromatin	normalnucleoli	mitoses	class
0	1002945	5	4	4	5	7	10.0	3	2	1	2
1	1015425	3	1	1	1	2	2.0	3	1	1	2
2	1016277	6	8	8	1	3	4.0	3	7	1	2
3	1017023	4	1	1	3	2	1.0	3	1	1	2
4	1017122	8	10	10	8	7	10.0	9	7	1	4
# Create a training/test set in the ratio 80/20
train_dataset = dataset.sample(frac=0.8,random_state=0)
test_dataset = dataset.drop(train_dataset.index)

# Set the training and test set
train_dataset1= train_dataset[['thickness','cellsize','cellshape','adhesion',
                'epicellsize', 'barenuclei', 'chromatin', 'normalnucleoli','mitoses']]
test_dataset1=test_dataset[['thickness','cellsize','cellshape','adhesion',
                'epicellsize', 'barenuclei', 'chromatin', 'normalnucleoli','mitoses']]
In [34]:
# Generate the stats for each column to be used for normalization
train_stats = train_dataset1.describe()
train_stats = train_stats.transpose()
train_stats
Out[34]:
count mean std min 25% 50% 75% max
thickness 546.0 4.430403 2.812768 1.0 2.0 4.0 6.0 10.0
cellsize 546.0 3.179487 3.083668 1.0 1.0 1.0 5.0 10.0
cellshape 546.0 3.225275 3.005588 1.0 1.0 1.0 5.0 10.0
adhesion 546.0 2.921245 2.937144 1.0 1.0 1.0 4.0 10.0
epicellsize 546.0 3.261905 2.252643 1.0 2.0 2.0 4.0 10.0
barenuclei 546.0 3.560440 3.651946 1.0 1.0 1.0 7.0 10.0
chromatin 546.0 3.483516 2.492687 1.0 2.0 3.0 5.0 10.0
normalnucleoli 546.0 2.875458 3.064305 1.0 1.0 1.0 4.0 10.0
mitoses 546.0 1.609890 1.736762 1.0 1.0 1.0 1.0 10.0
In [0]:
# Create target variables
train_labels = train_dataset.pop('class')
test_labels = test_dataset.pop('class')
In [0]:
# Set the target variables as 0 or 1
train_labels[train_labels==2] =0 # benign
train_labels[train_labels==4] =1 # malignant

test_labels[test_labels==2] =0 # benign
test_labels[test_labels==4] =1 # malignant
In [0]:
# Normalize by subtracting mean and dividing by standard deviation
def normalize(x):
  return (x - train_stats['mean']) / train_stats['std']

# Convert columns to numeric
train_dataset1 = train_dataset1.apply(pd.to_numeric)
test_dataset1 = test_dataset1.apply(pd.to_numeric)

# Normalize
normalized_train_data = normalize(train_dataset1)
normalized_test_data = normalize(test_dataset1)
In [0]:
# Create a model
model = tf.keras.Sequential([
    keras.layers.Dense(6, activation=tf.nn.relu, input_shape=[len(train_dataset1.keys())]),
    keras.layers.Dense(9, activation=tf.nn.relu),
    keras.layers.Dense(6,activation=tf.nn.relu),
    keras.layers.Dense(1)
  ])

# Use the RMSProp optimizer
optimizer = tf.keras.optimizers.RMSprop(0.01)

# Since this is binary classification use binary_crossentropy
model.compile(loss='binary_crossentropy',
                optimizer=optimizer,
                metrics=['acc'])


# Fit a model
history=model.fit(
  normalized_train_data, train_labels,
  epochs=1000, validation_data=(normalized_test_data,test_labels), verbose=0)
In [55]:
hist = pd.DataFrame(history.history)
hist['epoch'] = history.epoch
hist.tail()
loss acc val_loss val_acc epoch
995 0.112499 0.992674 0.454739 0.970588 995
996 0.112499 0.992674 0.454739 0.970588 996
997 0.112499 0.992674 0.454739 0.970588 997
998 0.112499 0.992674 0.454739 0.970588 998
999 0.112499 0.992674 0.454739 0.970588 999
In [58]:
# Plot training and test accuracy 
plt.plot(history.history['acc'])
plt.plot(history.history['val_acc'])
plt.title('model accuracy')
plt.ylabel('accuracy')
plt.xlabel('epoch')
plt.legend(['train', 'test'], loc='upper left')
plt.ylim([0.9,1])
plt.show()












# Plot training and test loss
plt.plot(history.history['loss'])
plt.plot(history.history['val_loss'])
plt.title('model loss')
plt.ylabel('loss')
plt.xlabel('epoch')
plt.legend(['train', 'test'], loc='upper left')
plt.ylim([0,0.5])
plt.show()


2a. Binary classification in Tensorflow -R

This is a simple binary classification problem from UCI Machine Learning repository and deals with data on Breast cancer from the Univ. of Wisconsin Breast Cancer Wisconsin (Diagnostic) Data Set

# Read the data for Breast cancer (Wisconsin)
dataset <- read.csv("https://archive.ics.uci.edu/ml/machine-learning-databases/breast-cancer-wisconsin/breast-cancer-wisconsin.data")

# Rename the columns
names(dataset) <- c("id","thickness",   "cellsize", "cellshape","adhesion","epicellsize",
                    "barenuclei","chromatin","normalnucleoli","mitoses","class")

# Remove the columns id and class
dataset1 <- subset(dataset, select = -c(id, class))
dataset2 <- na.omit(dataset1)

# Convert the column to numeric
dataset2$barenuclei <- as.numeric(dataset2$barenuclei)

Normalize the data

train_data <-apply(dataset2,2,normalize)
train_labels <- as.matrix(select(dataset,class))

# Set the target variables as 0 or 1 as it binary classification
train_labels[train_labels==2,]=0
train_labels[train_labels==4,]=1

Create the Deep Learning model

model <- keras_model_sequential()
model %>% 
  layer_dense(units = 6, activation = 'relu', input_shape = dim(train_data)[2]) %>% 
  layer_dense(units = 9, activation = 'relu') %>%
  layer_dense(units = 6, activation = 'relu') %>%
  layer_dense(units = 1)

# Since this is a binary classification we use binary cross entropy
model %>% compile(
  loss = 'binary_crossentropy',
  optimizer = optimizer_rmsprop(),
  metrics = c('accuracy')  # Metrics is accuracy
)

Fit the model. Use 20% of data for validation

history <- model %>% fit(
  train_data, train_labels, 
  epochs = 30, batch_size = 128, 
  validation_split = 0.2
)

Plot the accuracy and loss for training and validation data

plot(history)

3. MNIST in Tensorflow – Python

This takes the famous MNIST handwritten digits . It ca be seen that Tensorflow and Keras make short work of this famous problem of the late 1980s

# Download MNIST data
mnist=tf.keras.datasets.mnist
# Set training and test data and labels
(training_images,training_labels),(test_images,test_labels)=mnist.load_data()

print(training_images.shape)
print(test_images.shape)
(60000, 28, 28)
(10000, 28, 28)
In [61]:
# Plot a sample image from MNIST and show contents
import matplotlib.pyplot as plt
plt.imshow(training_images[1])
print(training_images[1])
[[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 51 159 253
159 50 0 0 0 0 0 0 0 0]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 48 238 252 252
252 237 0 0 0 0 0 0 0 0]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 54 227 253 252 239
233 252 57 6 0 0 0 0 0 0]
[ 0 0 0 0 0 0 0 0 0 0 0 10 60 224 252 253 252 202
84 252 253 122 0 0 0 0 0 0]
[ 0 0 0 0 0 0 0 0 0 0 0 163 252 252 252 253 252 252
96 189 253 167 0 0 0 0 0 0]
[ 0 0 0 0 0 0 0 0 0 0 51 238 253 253 190 114 253 228
47 79 255 168 0 0 0 0 0 0]
[ 0 0 0 0 0 0 0 0 0 48 238 252 252 179 12 75 121 21
0 0 253 243 50 0 0 0 0 0]
[ 0 0 0 0 0 0 0 0 38 165 253 233 208 84 0 0 0 0
0 0 253 252 165 0 0 0 0 0]
[ 0 0 0 0 0 0 0 7 178 252 240 71 19 28 0 0 0 0
0 0 253 252 195 0 0 0 0 0]
[ 0 0 0 0 0 0 0 57 252 252 63 0 0 0 0 0 0 0
0 0 253 252 195 0 0 0 0 0]
[ 0 0 0 0 0 0 0 198 253 190 0 0 0 0 0 0 0 0
0 0 255 253 196 0 0 0 0 0]
[ 0 0 0 0 0 0 76 246 252 112 0 0 0 0 0 0 0 0
0 0 253 252 148 0 0 0 0 0]
[ 0 0 0 0 0 0 85 252 230 25 0 0 0 0 0 0 0 0
7 135 253 186 12 0 0 0 0 0]
[ 0 0 0 0 0 0 85 252 223 0 0 0 0 0 0 0 0 7
131 252 225 71 0 0 0 0 0 0]
[ 0 0 0 0 0 0 85 252 145 0 0 0 0 0 0 0 48 165
252 173 0 0 0 0 0 0 0 0]
[ 0 0 0 0 0 0 86 253 225 0 0 0 0 0 0 114 238 253
162 0 0 0 0 0 0 0 0 0]
[ 0 0 0 0 0 0 85 252 249 146 48 29 85 178 225 253 223 167
56 0 0 0 0 0 0 0 0 0]
[ 0 0 0 0 0 0 85 252 252 252 229 215 252 252 252 196 130 0
0 0 0 0 0 0 0 0 0 0]
[ 0 0 0 0 0 0 28 199 252 252 253 252 252 233 145 0 0 0
0 0 0 0 0 0 0 0 0 0]
[ 0 0 0 0 0 0 0 25 128 252 253 252 141 37 0 0 0 0
0 0 0 0 0 0 0 0 0 0]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0]]


# Normalize the images by dividing by 255.0
training_images = training_images/255.0
test_images = test_images/255.0

# Create a Sequential Keras model
model = tf.keras.models.Sequential([tf.keras.layers.Flatten(),
                                   tf.keras.layers.Dense(1024,activation=tf.nn.relu),
                                   tf.keras.layers.Dense(10,activation=tf.nn.softmax)])
model.compile(optimizer='adam',loss='sparse_categorical_crossentropy',metrics=['accuracy'])
In [68]:
history=model.fit(training_images,training_labels,validation_data=(test_images, test_labels), epochs=5, verbose=1)
Train on 60000 samples, validate on 10000 samples
Epoch 1/5
60000/60000 [==============================] - 17s 291us/sample - loss: 0.0020 - acc: 0.9999 - val_loss: 0.0719 - val_acc: 0.9810
Epoch 2/5
60000/60000 [==============================] - 17s 284us/sample - loss: 0.0021 - acc: 0.9998 - val_loss: 0.0705 - val_acc: 0.9821
Epoch 3/5
60000/60000 [==============================] - 17s 286us/sample - loss: 0.0017 - acc: 0.9999 - val_loss: 0.0729 - val_acc: 0.9805
Epoch 4/5
60000/60000 [==============================] - 17s 284us/sample - loss: 0.0014 - acc: 0.9999 - val_loss: 0.0762 - val_acc: 0.9804
Epoch 5/5
60000/60000 [==============================] - 17s 280us/sample - loss: 0.0015 - acc: 0.9999 - val_loss: 0.0735 - val_acc: 0.9812

Fig 1

Fig 2

 

 

 

 

 

 

 

 

MNIST in Tensorflow – R

The following code uses Tensorflow to learn MNIST’s handwritten digits ### Load MNIST data

mnist <- dataset_mnist()
x_train <- mnist$train$x
y_train <- mnist$train$y
x_test <- mnist$test$x
y_test <- mnist$test$y

Reshape and rescale

# Reshape the array
x_train <- array_reshape(x_train, c(nrow(x_train), 784))
x_test <- array_reshape(x_test, c(nrow(x_test), 784))
# Rescale
x_train <- x_train / 255
x_test <- x_test / 255

Convert out put to One Hot encoded format

y_train <- to_categorical(y_train, 10)
y_test <- to_categorical(y_test, 10)

Fit the model

Use the softmax activation for recognizing 10 digits and categorical cross entropy for loss

model <- keras_model_sequential() 
model %>% 
  layer_dense(units = 256, activation = 'relu', input_shape = c(784)) %>% 
  layer_dense(units = 128, activation = 'relu') %>%
  layer_dense(units = 10, activation = 'softmax') # Use softmax

model %>% compile(
  loss = 'categorical_crossentropy',
  optimizer = optimizer_rmsprop(),
  metrics = c('accuracy')
)

Fit the model

Note: A smaller number of epochs has been used. For better performance increase number of epochs

history <- model %>% fit(
  x_train, y_train, 
  epochs = 5, batch_size = 128, 
  validation_data = list(x_test,y_test)
)