3 Deep learning

3.1 Deep neural network

3.1.1 Load data

# load the Pima Indians dataset from the mlbench dataset
library(mlbench)
data(PimaIndiansDiabetes) 
# rename dataset to have shorter name because lazy
diabetes <- PimaIndiansDiabetes

data.set <- diabetes
  # datatable(data.set[sample(nrow(data.set),
  #                         replace = FALSE,
  #                         size = 0.005 * nrow(data.set)), ])

summary(data.set)

##     pregnant         glucose         pressure         triceps     
##  Min.   : 0.000   Min.   :  0.0   Min.   :  0.00   Min.   : 0.00  
##  1st Qu.: 1.000   1st Qu.: 99.0   1st Qu.: 62.00   1st Qu.: 0.00  
##  Median : 3.000   Median :117.0   Median : 72.00   Median :23.00  
##  Mean   : 3.845   Mean   :120.9   Mean   : 69.11   Mean   :20.54  
##  3rd Qu.: 6.000   3rd Qu.:140.2   3rd Qu.: 80.00   3rd Qu.:32.00  
##  Max.   :17.000   Max.   :199.0   Max.   :122.00   Max.   :99.00  
##     insulin           mass          pedigree           age        diabetes 
##  Min.   :  0.0   Min.   : 0.00   Min.   :0.0780   Min.   :21.00   neg:500  
##  1st Qu.:  0.0   1st Qu.:27.30   1st Qu.:0.2437   1st Qu.:24.00   pos:268  
##  Median : 30.5   Median :32.00   Median :0.3725   Median :29.00            
##  Mean   : 79.8   Mean   :31.99   Mean   :0.4719   Mean   :33.24            
##  3rd Qu.:127.2   3rd Qu.:36.60   3rd Qu.:0.6262   3rd Qu.:41.00            
##  Max.   :846.0   Max.   :67.10   Max.   :2.4200   Max.   :81.00

3.1.2 Process data and variable

data.set$diabetes <- as.numeric(data.set$diabetes)
data.set$diabetes=data.set$diabetes-1
head(data.set$diabetes)

## [1] 1 0 1 0 1 0

head(data.set)

##   pregnant glucose pressure triceps insulin mass pedigree age diabetes
## 1        6     148       72      35       0 33.6    0.627  50        1
## 2        1      85       66      29       0 26.6    0.351  31        0
## 3        8     183       64       0       0 23.3    0.672  32        1
## 4        1      89       66      23      94 28.1    0.167  21        0
## 5        0     137       40      35     168 43.1    2.288  33        1
## 6        5     116       74       0       0 25.6    0.201  30        0

str(data.set)

## 'data.frame':    768 obs. of  9 variables:
##  $ pregnant: num  6 1 8 1 0 5 3 10 2 8 ...
##  $ glucose : num  148 85 183 89 137 116 78 115 197 125 ...
##  $ pressure: num  72 66 64 66 40 74 50 0 70 96 ...
##  $ triceps : num  35 29 0 23 35 0 32 0 45 0 ...
##  $ insulin : num  0 0 0 94 168 0 88 0 543 0 ...
##  $ mass    : num  33.6 26.6 23.3 28.1 43.1 25.6 31 35.3 30.5 0 ...
##  $ pedigree: num  0.627 0.351 0.672 0.167 2.288 ...
##  $ age     : num  50 31 32 21 33 30 26 29 53 54 ...
##  $ diabetes: num  1 0 1 0 1 0 1 0 1 1 ...

• transform dataframe into matrix

# Cast dataframe as a matrix
data.set <- as.matrix(data.set)

# Remove column names
dimnames(data.set) = NULL

head(data.set)

##      [,1] [,2] [,3] [,4] [,5] [,6]  [,7] [,8] [,9]
## [1,]    6  148   72   35    0 33.6 0.627   50    1
## [2,]    1   85   66   29    0 26.6 0.351   31    0
## [3,]    8  183   64    0    0 23.3 0.672   32    1
## [4,]    1   89   66   23   94 28.1 0.167   21    0
## [5,]    0  137   40   35  168 43.1 2.288   33    1
## [6,]    5  116   74    0    0 25.6 0.201   30    0

3.1.3 Split data into training and test datasets

• including xtrain ytrian xtest ytest

# Split for train and test data
set.seed(100)
indx <- sample(2,
               nrow(data.set),
               replace = TRUE,
               prob = c(0.8, 0.2)) # Makes index with values 1 and 2

# Select only the feature variables
# Take rows with index = 1
x_train <- data.set[indx == 1, 1:8]
x_test <- data.set[indx == 2, 1:8]

# Feature Scaling
x_train <- scale(x_train )
x_test <- scale(x_test )

y_test_actual <- data.set[indx == 2, 9]

• transform target as on-hot-coding format

# Using similar indices to correspond to the training and test set
y_train <- to_categorical(data.set[indx == 1, 9])
y_test <- to_categorical(data.set[indx == 2, 9])
head(y_train)

##      [,1] [,2]
## [1,]    0    1
## [2,]    1    0
## [3,]    0    1
## [4,]    1    0
## [5,]    0    1
## [6,]    1    0

head(data.set[indx == 1, 9],20)

##  [1] 1 0 1 0 1 0 0 1 1 0 0 1 1 1 1 1 0 1 0 0

• dimension of four splitting data sets

dim(x_train)

## [1] 609   8

dim(y_train)

## [1] 609   2

dim(x_test)

## [1] 159   8

dim(y_test)

## [1] 159   2

3.1.4 Creating neural network model

3.1.4.1 construction of model

• the output layer contains 3 levels

# Creating the model
model <- keras_model_sequential()

model %>% 
  layer_dense(name = "DeepLayer1",
              units = 10,
              activation = "relu",
              input_shape = c(8)) %>% 
  # input 4 features
  layer_dense(name = "DeepLayer2",
              units = 10,
              activation = "relu") %>% 
  
  layer_dense(name = "OutputLayer",
              units = 2,
              activation = "softmax")
  # output 4 categories using one-hot-coding
summary(model)

## Model: "sequential"
## ________________________________________________________________________________
##  Layer (type)                       Output Shape                    Param #     
## ================================================================================
##  DeepLayer1 (Dense)                 (None, 10)                      90          
##  DeepLayer2 (Dense)                 (None, 10)                      110         
##  OutputLayer (Dense)                (None, 2)                       22          
## ================================================================================
## Total params: 222
## Trainable params: 222
## Non-trainable params: 0
## ________________________________________________________________________________

3.1.4.2 Compiling the model

# Compiling the model
model %>% compile(loss = "categorical_crossentropy",
                  optimizer = "adam",
                  metrics = c("accuracy"))

3.1.4.3 Fitting the data and plot

history <- model %>% 
  fit(x_train,
      y_train,
      
      # adjusting number of epoch
      epoch = 60,
      
      # adjusting number of batch size
      batch_size = 64,
      validation_split = 0.15,
      verbose = 2)

## Epoch 1/60
## 9/9 - 0s - loss: 0.9681 - accuracy: 0.3636 - val_loss: 0.8513 - val_accuracy: 0.4457 - 489ms/epoch - 54ms/step
## Epoch 2/60
## 9/9 - 0s - loss: 0.8899 - accuracy: 0.3849 - val_loss: 0.7903 - val_accuracy: 0.5000 - 52ms/epoch - 6ms/step
## Epoch 3/60
## 9/9 - 0s - loss: 0.8272 - accuracy: 0.3926 - val_loss: 0.7470 - val_accuracy: 0.4783 - 42ms/epoch - 5ms/step
## Epoch 4/60
## 9/9 - 0s - loss: 0.7779 - accuracy: 0.4313 - val_loss: 0.7140 - val_accuracy: 0.5109 - 34ms/epoch - 4ms/step
## Epoch 5/60
## 9/9 - 0s - loss: 0.7395 - accuracy: 0.4603 - val_loss: 0.6874 - val_accuracy: 0.5109 - 44ms/epoch - 5ms/step
## Epoch 6/60
## 9/9 - 0s - loss: 0.7049 - accuracy: 0.5184 - val_loss: 0.6661 - val_accuracy: 0.5543 - 58ms/epoch - 6ms/step
## Epoch 7/60
## 9/9 - 0s - loss: 0.6775 - accuracy: 0.5629 - val_loss: 0.6490 - val_accuracy: 0.5652 - 55ms/epoch - 6ms/step
## Epoch 8/60
## 9/9 - 0s - loss: 0.6535 - accuracy: 0.6190 - val_loss: 0.6335 - val_accuracy: 0.6304 - 40ms/epoch - 4ms/step
## Epoch 9/60
## 9/9 - 0s - loss: 0.6348 - accuracy: 0.6441 - val_loss: 0.6211 - val_accuracy: 0.6630 - 39ms/epoch - 4ms/step
## Epoch 10/60
## 9/9 - 0s - loss: 0.6195 - accuracy: 0.6847 - val_loss: 0.6093 - val_accuracy: 0.6957 - 39ms/epoch - 4ms/step
## Epoch 11/60
## 9/9 - 0s - loss: 0.6055 - accuracy: 0.6925 - val_loss: 0.5989 - val_accuracy: 0.7065 - 39ms/epoch - 4ms/step
## Epoch 12/60
## 9/9 - 0s - loss: 0.5937 - accuracy: 0.6963 - val_loss: 0.5898 - val_accuracy: 0.6957 - 45ms/epoch - 5ms/step
## Epoch 13/60
## 9/9 - 0s - loss: 0.5824 - accuracy: 0.7041 - val_loss: 0.5820 - val_accuracy: 0.6848 - 57ms/epoch - 6ms/step
## Epoch 14/60
## 9/9 - 0s - loss: 0.5737 - accuracy: 0.7002 - val_loss: 0.5761 - val_accuracy: 0.6957 - 42ms/epoch - 5ms/step
## Epoch 15/60
## 9/9 - 0s - loss: 0.5659 - accuracy: 0.7002 - val_loss: 0.5706 - val_accuracy: 0.6739 - 37ms/epoch - 4ms/step
## Epoch 16/60
## 9/9 - 0s - loss: 0.5590 - accuracy: 0.6983 - val_loss: 0.5650 - val_accuracy: 0.6739 - 36ms/epoch - 4ms/step
## Epoch 17/60
## 9/9 - 0s - loss: 0.5528 - accuracy: 0.7060 - val_loss: 0.5606 - val_accuracy: 0.6957 - 46ms/epoch - 5ms/step
## Epoch 18/60
## 9/9 - 0s - loss: 0.5478 - accuracy: 0.7176 - val_loss: 0.5548 - val_accuracy: 0.7174 - 45ms/epoch - 5ms/step
## Epoch 19/60
## 9/9 - 0s - loss: 0.5427 - accuracy: 0.7234 - val_loss: 0.5502 - val_accuracy: 0.7174 - 47ms/epoch - 5ms/step
## Epoch 20/60
## 9/9 - 0s - loss: 0.5385 - accuracy: 0.7234 - val_loss: 0.5465 - val_accuracy: 0.7283 - 47ms/epoch - 5ms/step
## Epoch 21/60
## 9/9 - 0s - loss: 0.5347 - accuracy: 0.7157 - val_loss: 0.5429 - val_accuracy: 0.7283 - 72ms/epoch - 8ms/step
## Epoch 22/60
## 9/9 - 0s - loss: 0.5308 - accuracy: 0.7215 - val_loss: 0.5398 - val_accuracy: 0.7283 - 50ms/epoch - 6ms/step
## Epoch 23/60
## 9/9 - 0s - loss: 0.5273 - accuracy: 0.7234 - val_loss: 0.5371 - val_accuracy: 0.7391 - 45ms/epoch - 5ms/step
## Epoch 24/60
## 9/9 - 0s - loss: 0.5241 - accuracy: 0.7234 - val_loss: 0.5341 - val_accuracy: 0.7391 - 58ms/epoch - 6ms/step
## Epoch 25/60
## 9/9 - 0s - loss: 0.5210 - accuracy: 0.7311 - val_loss: 0.5318 - val_accuracy: 0.7174 - 41ms/epoch - 5ms/step
## Epoch 26/60
## 9/9 - 0s - loss: 0.5187 - accuracy: 0.7350 - val_loss: 0.5303 - val_accuracy: 0.7174 - 42ms/epoch - 5ms/step
## Epoch 27/60
## 9/9 - 0s - loss: 0.5165 - accuracy: 0.7311 - val_loss: 0.5288 - val_accuracy: 0.7174 - 45ms/epoch - 5ms/step
## Epoch 28/60
## 9/9 - 0s - loss: 0.5142 - accuracy: 0.7369 - val_loss: 0.5273 - val_accuracy: 0.7174 - 65ms/epoch - 7ms/step
## Epoch 29/60
## 9/9 - 0s - loss: 0.5117 - accuracy: 0.7389 - val_loss: 0.5259 - val_accuracy: 0.7174 - 50ms/epoch - 6ms/step
## Epoch 30/60
## 9/9 - 0s - loss: 0.5097 - accuracy: 0.7389 - val_loss: 0.5248 - val_accuracy: 0.7391 - 47ms/epoch - 5ms/step
## Epoch 31/60
## 9/9 - 0s - loss: 0.5081 - accuracy: 0.7389 - val_loss: 0.5245 - val_accuracy: 0.7391 - 44ms/epoch - 5ms/step
## Epoch 32/60
## 9/9 - 0s - loss: 0.5059 - accuracy: 0.7369 - val_loss: 0.5243 - val_accuracy: 0.7391 - 48ms/epoch - 5ms/step
## Epoch 33/60
## 9/9 - 0s - loss: 0.5038 - accuracy: 0.7350 - val_loss: 0.5242 - val_accuracy: 0.7283 - 42ms/epoch - 5ms/step
## Epoch 34/60
## 9/9 - 0s - loss: 0.5018 - accuracy: 0.7369 - val_loss: 0.5242 - val_accuracy: 0.7283 - 61ms/epoch - 7ms/step
## Epoch 35/60
## 9/9 - 0s - loss: 0.5003 - accuracy: 0.7369 - val_loss: 0.5238 - val_accuracy: 0.7283 - 54ms/epoch - 6ms/step
## Epoch 36/60
## 9/9 - 0s - loss: 0.4988 - accuracy: 0.7408 - val_loss: 0.5237 - val_accuracy: 0.7283 - 48ms/epoch - 5ms/step
## Epoch 37/60
## 9/9 - 0s - loss: 0.4977 - accuracy: 0.7485 - val_loss: 0.5234 - val_accuracy: 0.7283 - 40ms/epoch - 4ms/step
## Epoch 38/60
## 9/9 - 0s - loss: 0.4961 - accuracy: 0.7524 - val_loss: 0.5232 - val_accuracy: 0.7174 - 42ms/epoch - 5ms/step
## Epoch 39/60
## 9/9 - 0s - loss: 0.4948 - accuracy: 0.7466 - val_loss: 0.5227 - val_accuracy: 0.7283 - 39ms/epoch - 4ms/step
## Epoch 40/60
## 9/9 - 0s - loss: 0.4934 - accuracy: 0.7524 - val_loss: 0.5227 - val_accuracy: 0.7174 - 39ms/epoch - 4ms/step
## Epoch 41/60
## 9/9 - 0s - loss: 0.4919 - accuracy: 0.7544 - val_loss: 0.5231 - val_accuracy: 0.7391 - 45ms/epoch - 5ms/step
## Epoch 42/60
## 9/9 - 0s - loss: 0.4903 - accuracy: 0.7524 - val_loss: 0.5228 - val_accuracy: 0.7500 - 40ms/epoch - 4ms/step
## Epoch 43/60
## 9/9 - 0s - loss: 0.4892 - accuracy: 0.7563 - val_loss: 0.5223 - val_accuracy: 0.7391 - 33ms/epoch - 4ms/step
## Epoch 44/60
## 9/9 - 0s - loss: 0.4882 - accuracy: 0.7582 - val_loss: 0.5221 - val_accuracy: 0.7391 - 37ms/epoch - 4ms/step
## Epoch 45/60
## 9/9 - 0s - loss: 0.4876 - accuracy: 0.7582 - val_loss: 0.5220 - val_accuracy: 0.7500 - 44ms/epoch - 5ms/step
## Epoch 46/60
## 9/9 - 0s - loss: 0.4862 - accuracy: 0.7640 - val_loss: 0.5213 - val_accuracy: 0.7391 - 43ms/epoch - 5ms/step
## Epoch 47/60
## 9/9 - 0s - loss: 0.4843 - accuracy: 0.7640 - val_loss: 0.5209 - val_accuracy: 0.7391 - 33ms/epoch - 4ms/step
## Epoch 48/60
## 9/9 - 0s - loss: 0.4830 - accuracy: 0.7640 - val_loss: 0.5212 - val_accuracy: 0.7500 - 35ms/epoch - 4ms/step
## Epoch 49/60
## 9/9 - 0s - loss: 0.4820 - accuracy: 0.7698 - val_loss: 0.5218 - val_accuracy: 0.7391 - 35ms/epoch - 4ms/step
## Epoch 50/60
## 9/9 - 0s - loss: 0.4806 - accuracy: 0.7660 - val_loss: 0.5224 - val_accuracy: 0.7391 - 37ms/epoch - 4ms/step
## Epoch 51/60
## 9/9 - 0s - loss: 0.4796 - accuracy: 0.7698 - val_loss: 0.5224 - val_accuracy: 0.7500 - 39ms/epoch - 4ms/step
## Epoch 52/60
## 9/9 - 0s - loss: 0.4780 - accuracy: 0.7718 - val_loss: 0.5229 - val_accuracy: 0.7500 - 35ms/epoch - 4ms/step
## Epoch 53/60
## 9/9 - 0s - loss: 0.4775 - accuracy: 0.7718 - val_loss: 0.5224 - val_accuracy: 0.7391 - 36ms/epoch - 4ms/step
## Epoch 54/60
## 9/9 - 0s - loss: 0.4762 - accuracy: 0.7737 - val_loss: 0.5221 - val_accuracy: 0.7391 - 37ms/epoch - 4ms/step
## Epoch 55/60
## 9/9 - 0s - loss: 0.4755 - accuracy: 0.7756 - val_loss: 0.5212 - val_accuracy: 0.7391 - 36ms/epoch - 4ms/step
## Epoch 56/60
## 9/9 - 0s - loss: 0.4741 - accuracy: 0.7756 - val_loss: 0.5209 - val_accuracy: 0.7500 - 32ms/epoch - 4ms/step
## Epoch 57/60
## 9/9 - 0s - loss: 0.4731 - accuracy: 0.7756 - val_loss: 0.5209 - val_accuracy: 0.7609 - 34ms/epoch - 4ms/step
## Epoch 58/60
## 9/9 - 0s - loss: 0.4720 - accuracy: 0.7776 - val_loss: 0.5192 - val_accuracy: 0.7500 - 39ms/epoch - 4ms/step
## Epoch 59/60
## 9/9 - 0s - loss: 0.4711 - accuracy: 0.7776 - val_loss: 0.5188 - val_accuracy: 0.7500 - 36ms/epoch - 4ms/step
## Epoch 60/60
## 9/9 - 0s - loss: 0.4699 - accuracy: 0.7814 - val_loss: 0.5187 - val_accuracy: 0.7609 - 36ms/epoch - 4ms/step

plot(history)

3.1.5 Evaluation

3.1.5.1 Output loss and accuracy

using xtest and ytest data sets to evaluate the built model directly

model %>% 
  evaluate(x_test,
           y_test)

## 
## 1/5 [=====>........................] - ETA: 0s - loss: 0.4753 - accuracy: 0.8125
## 5/5 [==============================] - 0s 1ms/step - loss: 0.4506 - accuracy: 0.7925

##      loss  accuracy 
## 0.4506253 0.7924528

3.1.5.2 Output the predicted classes and confusion matrix

pred <- model %>% 
  predict(x_test) %>% k_argmax() %>% k_get_value()
head(pred)

## [1] 0 1 0 1 0 0

table(Predicted = pred,
      Actual = y_test_actual)

##          Actual
## Predicted  0  1
##         0 92 21
##         1 12 34

3.1.5.3 Output the predicted values

prob <- model %>% 
  predict(x_test) %>% k_get_value()
head(prob)

##           [,1]       [,2]
## [1,] 0.9680360 0.03196405
## [2,] 0.2276911 0.77230895
## [3,] 0.9635938 0.03640625
## [4,] 0.3521949 0.64780515
## [5,] 0.9190423 0.08095762
## [6,] 0.7750926 0.22490738

3.1.5.4 Comparison between prob, pred, and ytest

comparison <- cbind(prob ,
      pred ,
      y_test_actual )
head(comparison)

##                           pred y_test_actual
## [1,] 0.9680360 0.03196405    0             1
## [2,] 0.2276911 0.77230895    1             1
## [3,] 0.9635938 0.03640625    0             0
## [4,] 0.3521949 0.64780515    1             1
## [5,] 0.9190423 0.08095762    0             0
## [6,] 0.7750926 0.22490738    0             0

3.2 Deep neural networks for regression

3.2.1 Loading packages and data sets

library(readr)
library(keras)
library(plotly)

data("Boston", package = "MASS")
data.set <- Boston

dim(data.set)

## [1] 506  14

3.2.2 Convert dataframe to matrix without dimnames

library(DT)
 
# Cast dataframe as a matrix
data.set <- as.matrix(data.set)
# Remove column names
dimnames(data.set) = NULL
head(data.set)

##         [,1] [,2] [,3] [,4]  [,5]  [,6] [,7]   [,8] [,9] [,10] [,11]  [,12]
## [1,] 0.00632   18 2.31    0 0.538 6.575 65.2 4.0900    1   296  15.3 396.90
## [2,] 0.02731    0 7.07    0 0.469 6.421 78.9 4.9671    2   242  17.8 396.90
## [3,] 0.02729    0 7.07    0 0.469 7.185 61.1 4.9671    2   242  17.8 392.83
## [4,] 0.03237    0 2.18    0 0.458 6.998 45.8 6.0622    3   222  18.7 394.63
## [5,] 0.06905    0 2.18    0 0.458 7.147 54.2 6.0622    3   222  18.7 396.90
## [6,] 0.02985    0 2.18    0 0.458 6.430 58.7 6.0622    3   222  18.7 394.12
##      [,13] [,14]
## [1,]  4.98  24.0
## [2,]  9.14  21.6
## [3,]  4.03  34.7
## [4,]  2.94  33.4
## [5,]  5.33  36.2
## [6,]  5.21  28.7

summary(data.set[, 14])

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##    5.00   17.02   21.20   22.53   25.00   50.00

 hist( data.set[, 14])

(#fig:target variable histogram)Fig 1 Histogram of the target variable

3.2.3 Spiting training and test data

# Split for train and test data
set.seed(123)
indx <- sample(2,
               nrow(data.set),
               replace = TRUE,
               prob = c(0.75, 0.25)) # Makes index with values 1 and 2

x_train <- data.set[indx == 1, 1:13]
x_test <- data.set[indx == 2, 1:13]
y_train <- data.set[indx == 1, 14]
y_test <- data.set[indx == 2, 14]

3.2.4 Normalizing xtrain and xtest data

x_train <- scale(x_train)
x_test <- scale(x_test)

3.2.5 Creating the model

model <- keras_model_sequential() %>% 
  layer_dense(units = 25,
              activation = "relu",
              input_shape = c(13)) %>% 
  layer_dropout(0.2) %>% 
  layer_dense(units = 25,
              activation = "relu") %>% 
  layer_dropout(0.2) %>% 
  layer_dense(units = 25,
              activation = "relu") %>% 
  layer_dropout(0.2) %>% 
  layer_dense(units = 1)

model %>% summary()

## Model: "sequential_1"
## ________________________________________________________________________________
##  Layer (type)                       Output Shape                    Param #     
## ================================================================================
##  dense_3 (Dense)                    (None, 25)                      350         
##  dropout_2 (Dropout)                (None, 25)                      0           
##  dense_2 (Dense)                    (None, 25)                      650         
##  dropout_1 (Dropout)                (None, 25)                      0           
##  dense_1 (Dense)                    (None, 25)                      650         
##  dropout (Dropout)                  (None, 25)                      0           
##  dense (Dense)                      (None, 1)                       26          
## ================================================================================
## Total params: 1,676
## Trainable params: 1,676
## Non-trainable params: 0
## ________________________________________________________________________________

model %>% get_config()

## {'name': 'sequential_1', 'layers': [{'class_name': 'InputLayer', 'config': {'batch_input_shape': (None, 13), 'dtype': 'float32', 'sparse': False, 'ragged': False, 'name': 'dense_3_input'}}, {'class_name': 'Dense', 'config': {'name': 'dense_3', 'trainable': True, 'batch_input_shape': (None, 13), 'dtype': 'float32', 'units': 25, 'activation': 'relu', 'use_bias': True, 'kernel_initializer': {'class_name': 'GlorotUniform', 'config': {'seed': None}}, 'bias_initializer': {'class_name': 'Zeros', 'config': {}}, 'kernel_regularizer': None, 'bias_regularizer': None, 'activity_regularizer': None, 'kernel_constraint': None, 'bias_constraint': None}}, {'class_name': 'Dropout', 'config': {'name': 'dropout_2', 'trainable': True, 'dtype': 'float32', 'rate': 0.2, 'noise_shape': None, 'seed': None}}, {'class_name': 'Dense', 'config': {'name': 'dense_2', 'trainable': True, 'dtype': 'float32', 'units': 25, 'activation': 'relu', 'use_bias': True, 'kernel_initializer': {'class_name': 'GlorotUniform', 'config': {'seed': None}}, 'bias_initializer': {'class_name': 'Zeros', 'config': {}}, 'kernel_regularizer': None, 'bias_regularizer': None, 'activity_regularizer': None, 'kernel_constraint': None, 'bias_constraint': None}}, {'class_name': 'Dropout', 'config': {'name': 'dropout_1', 'trainable': True, 'dtype': 'float32', 'rate': 0.2, 'noise_shape': None, 'seed': None}}, {'class_name': 'Dense', 'config': {'name': 'dense_1', 'trainable': True, 'dtype': 'float32', 'units': 25, 'activation': 'relu', 'use_bias': True, 'kernel_initializer': {'class_name': 'GlorotUniform', 'config': {'seed': None}}, 'bias_initializer': {'class_name': 'Zeros', 'config': {}}, 'kernel_regularizer': None, 'bias_regularizer': None, 'activity_regularizer': None, 'kernel_constraint': None, 'bias_constraint': None}}, {'class_name': 'Dropout', 'config': {'name': 'dropout', 'trainable': True, 'dtype': 'float32', 'rate': 0.2, 'noise_shape': None, 'seed': None}}, {'class_name': 'Dense', 'config': {'name': 'dense', 'trainable': True, 'dtype': 'float32', 'units': 1, 'activation': 'linear', 'use_bias': True, 'kernel_initializer': {'class_name': 'GlorotUniform', 'config': {'seed': None}}, 'bias_initializer': {'class_name': 'Zeros', 'config': {}}, 'kernel_regularizer': None, 'bias_regularizer': None, 'activity_regularizer': None, 'kernel_constraint': None, 'bias_constraint': None}}]}

3.2.6 Compiling the model

model %>% compile(loss = "mse",
                  optimizer = optimizer_rmsprop(),
                  metrics = c("mean_absolute_error"))

3.2.7 Fitting the model

history <- model %>% 
  fit(x_train,
      y_train,
      epoch = 100,
      batch_size = 64,
      validation_split = 0.1,
      callbacks = c(callback_early_stopping(monitor = "val_mean_absolute_error",
                                            patience = 5)),
      verbose = 2)

## Epoch 1/100
## 6/6 - 1s - loss: 633.1686 - mean_absolute_error: 23.1448 - val_loss: 362.1218 - val_mean_absolute_error: 18.6922 - 543ms/epoch - 90ms/step
## Epoch 2/100
## 6/6 - 0s - loss: 619.5684 - mean_absolute_error: 22.8226 - val_loss: 353.5802 - val_mean_absolute_error: 18.4510 - 29ms/epoch - 5ms/step
## Epoch 3/100
## 6/6 - 0s - loss: 606.3226 - mean_absolute_error: 22.4991 - val_loss: 343.4781 - val_mean_absolute_error: 18.1589 - 28ms/epoch - 5ms/step
## Epoch 4/100
## 6/6 - 0s - loss: 591.8018 - mean_absolute_error: 22.1299 - val_loss: 331.8621 - val_mean_absolute_error: 17.8183 - 29ms/epoch - 5ms/step
## Epoch 5/100
## 6/6 - 0s - loss: 575.3328 - mean_absolute_error: 21.7065 - val_loss: 318.4845 - val_mean_absolute_error: 17.4185 - 28ms/epoch - 5ms/step
## Epoch 6/100
## 6/6 - 0s - loss: 556.1640 - mean_absolute_error: 21.2277 - val_loss: 303.3835 - val_mean_absolute_error: 16.9556 - 29ms/epoch - 5ms/step
## Epoch 7/100
## 6/6 - 0s - loss: 527.6621 - mean_absolute_error: 20.5617 - val_loss: 285.5919 - val_mean_absolute_error: 16.3955 - 30ms/epoch - 5ms/step
## Epoch 8/100
## 6/6 - 0s - loss: 506.4395 - mean_absolute_error: 20.0282 - val_loss: 267.2332 - val_mean_absolute_error: 15.7963 - 30ms/epoch - 5ms/step
## Epoch 9/100
## 6/6 - 0s - loss: 469.5865 - mean_absolute_error: 19.0669 - val_loss: 247.6484 - val_mean_absolute_error: 15.1307 - 33ms/epoch - 5ms/step
## Epoch 10/100
## 6/6 - 0s - loss: 429.0699 - mean_absolute_error: 18.1442 - val_loss: 227.3992 - val_mean_absolute_error: 14.4101 - 35ms/epoch - 6ms/step
## Epoch 11/100
## 6/6 - 0s - loss: 388.9806 - mean_absolute_error: 17.1307 - val_loss: 205.8531 - val_mean_absolute_error: 13.6039 - 29ms/epoch - 5ms/step
## Epoch 12/100
## 6/6 - 0s - loss: 345.7701 - mean_absolute_error: 16.0031 - val_loss: 185.8886 - val_mean_absolute_error: 12.8119 - 31ms/epoch - 5ms/step
## Epoch 13/100
## 6/6 - 0s - loss: 310.5396 - mean_absolute_error: 14.8583 - val_loss: 166.5514 - val_mean_absolute_error: 12.0074 - 37ms/epoch - 6ms/step
## Epoch 14/100
## 6/6 - 0s - loss: 265.3821 - mean_absolute_error: 13.4096 - val_loss: 146.0776 - val_mean_absolute_error: 11.0859 - 46ms/epoch - 8ms/step
## Epoch 15/100
## 6/6 - 0s - loss: 220.2564 - mean_absolute_error: 12.1002 - val_loss: 126.8281 - val_mean_absolute_error: 10.1527 - 37ms/epoch - 6ms/step
## Epoch 16/100
## 6/6 - 0s - loss: 193.3011 - mean_absolute_error: 11.1827 - val_loss: 110.3338 - val_mean_absolute_error: 9.3306 - 37ms/epoch - 6ms/step
## Epoch 17/100
## 6/6 - 0s - loss: 152.6866 - mean_absolute_error: 9.6193 - val_loss: 94.0219 - val_mean_absolute_error: 8.5289 - 31ms/epoch - 5ms/step
## Epoch 18/100
## 6/6 - 0s - loss: 143.4529 - mean_absolute_error: 9.3241 - val_loss: 82.9254 - val_mean_absolute_error: 7.9897 - 29ms/epoch - 5ms/step
## Epoch 19/100
## 6/6 - 0s - loss: 108.7542 - mean_absolute_error: 7.8017 - val_loss: 75.9578 - val_mean_absolute_error: 7.6571 - 28ms/epoch - 5ms/step
## Epoch 20/100
## 6/6 - 0s - loss: 112.6149 - mean_absolute_error: 7.8218 - val_loss: 67.7028 - val_mean_absolute_error: 7.2327 - 29ms/epoch - 5ms/step
## Epoch 21/100
## 6/6 - 0s - loss: 94.2892 - mean_absolute_error: 7.1888 - val_loss: 65.4072 - val_mean_absolute_error: 7.0785 - 28ms/epoch - 5ms/step
## Epoch 22/100
## 6/6 - 0s - loss: 95.8447 - mean_absolute_error: 7.0795 - val_loss: 60.8710 - val_mean_absolute_error: 6.7702 - 30ms/epoch - 5ms/step
## Epoch 23/100
## 6/6 - 0s - loss: 81.0740 - mean_absolute_error: 6.7073 - val_loss: 58.3951 - val_mean_absolute_error: 6.5841 - 30ms/epoch - 5ms/step
## Epoch 24/100
## 6/6 - 0s - loss: 70.8558 - mean_absolute_error: 6.4321 - val_loss: 56.3403 - val_mean_absolute_error: 6.4243 - 31ms/epoch - 5ms/step
## Epoch 25/100
## 6/6 - 0s - loss: 86.6767 - mean_absolute_error: 6.9435 - val_loss: 52.0283 - val_mean_absolute_error: 6.0943 - 29ms/epoch - 5ms/step
## Epoch 26/100
## 6/6 - 0s - loss: 75.3748 - mean_absolute_error: 6.4401 - val_loss: 51.1953 - val_mean_absolute_error: 6.0465 - 29ms/epoch - 5ms/step
## Epoch 27/100
## 6/6 - 0s - loss: 67.8355 - mean_absolute_error: 6.0516 - val_loss: 54.1734 - val_mean_absolute_error: 6.2449 - 29ms/epoch - 5ms/step
## Epoch 28/100
## 6/6 - 0s - loss: 77.4505 - mean_absolute_error: 6.6767 - val_loss: 54.5568 - val_mean_absolute_error: 6.2994 - 28ms/epoch - 5ms/step
## Epoch 29/100
## 6/6 - 0s - loss: 61.7278 - mean_absolute_error: 5.7904 - val_loss: 51.2587 - val_mean_absolute_error: 6.1204 - 28ms/epoch - 5ms/step
## Epoch 30/100
## 6/6 - 0s - loss: 71.2910 - mean_absolute_error: 6.3351 - val_loss: 52.1180 - val_mean_absolute_error: 6.2051 - 29ms/epoch - 5ms/step
## Epoch 31/100
## 6/6 - 0s - loss: 68.1252 - mean_absolute_error: 6.1091 - val_loss: 47.0658 - val_mean_absolute_error: 5.8783 - 29ms/epoch - 5ms/step
## Epoch 32/100
## 6/6 - 0s - loss: 58.1343 - mean_absolute_error: 5.8253 - val_loss: 46.6667 - val_mean_absolute_error: 5.8744 - 30ms/epoch - 5ms/step
## Epoch 33/100
## 6/6 - 0s - loss: 57.8563 - mean_absolute_error: 5.6244 - val_loss: 44.8589 - val_mean_absolute_error: 5.7674 - 30ms/epoch - 5ms/step
## Epoch 34/100
## 6/6 - 0s - loss: 63.9937 - mean_absolute_error: 5.9953 - val_loss: 43.0551 - val_mean_absolute_error: 5.6553 - 31ms/epoch - 5ms/step
## Epoch 35/100
## 6/6 - 0s - loss: 63.4491 - mean_absolute_error: 5.9678 - val_loss: 41.5887 - val_mean_absolute_error: 5.5499 - 28ms/epoch - 5ms/step
## Epoch 36/100
## 6/6 - 0s - loss: 64.7595 - mean_absolute_error: 5.8879 - val_loss: 38.9553 - val_mean_absolute_error: 5.3575 - 32ms/epoch - 5ms/step
## Epoch 37/100
## 6/6 - 0s - loss: 63.6228 - mean_absolute_error: 5.9375 - val_loss: 39.8530 - val_mean_absolute_error: 5.4718 - 29ms/epoch - 5ms/step
## Epoch 38/100
## 6/6 - 0s - loss: 62.6301 - mean_absolute_error: 5.7237 - val_loss: 37.3205 - val_mean_absolute_error: 5.2747 - 29ms/epoch - 5ms/step
## Epoch 39/100
## 6/6 - 0s - loss: 60.3906 - mean_absolute_error: 5.7724 - val_loss: 35.2879 - val_mean_absolute_error: 5.1099 - 29ms/epoch - 5ms/step
## Epoch 40/100
## 6/6 - 0s - loss: 52.7585 - mean_absolute_error: 5.4360 - val_loss: 34.7210 - val_mean_absolute_error: 5.0942 - 30ms/epoch - 5ms/step
## Epoch 41/100
## 6/6 - 0s - loss: 51.7187 - mean_absolute_error: 5.2884 - val_loss: 30.2621 - val_mean_absolute_error: 4.7098 - 29ms/epoch - 5ms/step
## Epoch 42/100
## 6/6 - 0s - loss: 53.5071 - mean_absolute_error: 5.4761 - val_loss: 28.5758 - val_mean_absolute_error: 4.5740 - 30ms/epoch - 5ms/step
## Epoch 43/100
## 6/6 - 0s - loss: 52.8232 - mean_absolute_error: 5.5496 - val_loss: 28.6857 - val_mean_absolute_error: 4.5879 - 34ms/epoch - 6ms/step
## Epoch 44/100
## 6/6 - 0s - loss: 49.7628 - mean_absolute_error: 5.2005 - val_loss: 28.9877 - val_mean_absolute_error: 4.6011 - 30ms/epoch - 5ms/step
## Epoch 45/100
## 6/6 - 0s - loss: 51.1762 - mean_absolute_error: 5.3729 - val_loss: 27.6649 - val_mean_absolute_error: 4.5036 - 30ms/epoch - 5ms/step
## Epoch 46/100
## 6/6 - 0s - loss: 56.5504 - mean_absolute_error: 5.7260 - val_loss: 25.6642 - val_mean_absolute_error: 4.3385 - 27ms/epoch - 5ms/step
## Epoch 47/100
## 6/6 - 0s - loss: 51.8396 - mean_absolute_error: 5.1717 - val_loss: 26.9569 - val_mean_absolute_error: 4.4545 - 28ms/epoch - 5ms/step
## Epoch 48/100
## 6/6 - 0s - loss: 44.6086 - mean_absolute_error: 5.2793 - val_loss: 24.8331 - val_mean_absolute_error: 4.2759 - 30ms/epoch - 5ms/step
## Epoch 49/100
## 6/6 - 0s - loss: 44.1259 - mean_absolute_error: 4.8670 - val_loss: 23.5274 - val_mean_absolute_error: 4.1741 - 30ms/epoch - 5ms/step
## Epoch 50/100
## 6/6 - 0s - loss: 50.5595 - mean_absolute_error: 5.1824 - val_loss: 21.8385 - val_mean_absolute_error: 4.0405 - 33ms/epoch - 5ms/step
## Epoch 51/100
## 6/6 - 0s - loss: 49.8013 - mean_absolute_error: 5.3196 - val_loss: 23.6437 - val_mean_absolute_error: 4.1954 - 29ms/epoch - 5ms/step
## Epoch 52/100
## 6/6 - 0s - loss: 47.3392 - mean_absolute_error: 5.1700 - val_loss: 21.5459 - val_mean_absolute_error: 4.0008 - 29ms/epoch - 5ms/step
## Epoch 53/100
## 6/6 - 0s - loss: 49.1827 - mean_absolute_error: 5.3445 - val_loss: 22.0266 - val_mean_absolute_error: 4.0278 - 29ms/epoch - 5ms/step
## Epoch 54/100
## 6/6 - 0s - loss: 49.9451 - mean_absolute_error: 5.2521 - val_loss: 23.2426 - val_mean_absolute_error: 4.1344 - 29ms/epoch - 5ms/step
## Epoch 55/100
## 6/6 - 0s - loss: 48.2228 - mean_absolute_error: 5.2593 - val_loss: 22.7446 - val_mean_absolute_error: 4.0828 - 29ms/epoch - 5ms/step
## Epoch 56/100
## 6/6 - 0s - loss: 47.5721 - mean_absolute_error: 4.9321 - val_loss: 20.9730 - val_mean_absolute_error: 3.9223 - 29ms/epoch - 5ms/step
## Epoch 57/100
## 6/6 - 0s - loss: 49.8960 - mean_absolute_error: 4.9387 - val_loss: 19.2941 - val_mean_absolute_error: 3.7518 - 28ms/epoch - 5ms/step
## Epoch 58/100
## 6/6 - 0s - loss: 43.6015 - mean_absolute_error: 4.9093 - val_loss: 20.2174 - val_mean_absolute_error: 3.8490 - 28ms/epoch - 5ms/step
## Epoch 59/100
## 6/6 - 0s - loss: 49.6302 - mean_absolute_error: 5.1938 - val_loss: 19.3697 - val_mean_absolute_error: 3.7527 - 30ms/epoch - 5ms/step
## Epoch 60/100
## 6/6 - 0s - loss: 44.7460 - mean_absolute_error: 5.0207 - val_loss: 17.5183 - val_mean_absolute_error: 3.5735 - 29ms/epoch - 5ms/step
## Epoch 61/100
## 6/6 - 0s - loss: 45.6789 - mean_absolute_error: 5.0399 - val_loss: 17.6852 - val_mean_absolute_error: 3.5582 - 29ms/epoch - 5ms/step
## Epoch 62/100
## 6/6 - 0s - loss: 41.7331 - mean_absolute_error: 4.8633 - val_loss: 17.3254 - val_mean_absolute_error: 3.5304 - 31ms/epoch - 5ms/step
## Epoch 63/100
## 6/6 - 0s - loss: 44.0637 - mean_absolute_error: 5.0094 - val_loss: 15.9025 - val_mean_absolute_error: 3.3479 - 33ms/epoch - 6ms/step
## Epoch 64/100
## 6/6 - 0s - loss: 50.0619 - mean_absolute_error: 5.1017 - val_loss: 16.0546 - val_mean_absolute_error: 3.3891 - 33ms/epoch - 5ms/step
## Epoch 65/100
## 6/6 - 0s - loss: 54.1918 - mean_absolute_error: 5.3302 - val_loss: 15.3276 - val_mean_absolute_error: 3.2750 - 33ms/epoch - 6ms/step
## Epoch 66/100
## 6/6 - 0s - loss: 45.8594 - mean_absolute_error: 5.0630 - val_loss: 16.5450 - val_mean_absolute_error: 3.4201 - 29ms/epoch - 5ms/step
## Epoch 67/100
## 6/6 - 0s - loss: 37.5054 - mean_absolute_error: 4.6813 - val_loss: 15.5897 - val_mean_absolute_error: 3.2986 - 32ms/epoch - 5ms/step
## Epoch 68/100
## 6/6 - 0s - loss: 41.1114 - mean_absolute_error: 4.7638 - val_loss: 14.9583 - val_mean_absolute_error: 3.2099 - 39ms/epoch - 6ms/step
## Epoch 69/100
## 6/6 - 0s - loss: 42.1530 - mean_absolute_error: 4.7229 - val_loss: 14.8981 - val_mean_absolute_error: 3.2077 - 30ms/epoch - 5ms/step
## Epoch 70/100
## 6/6 - 0s - loss: 36.7822 - mean_absolute_error: 4.6359 - val_loss: 14.9601 - val_mean_absolute_error: 3.2092 - 30ms/epoch - 5ms/step
## Epoch 71/100
## 6/6 - 0s - loss: 42.6609 - mean_absolute_error: 4.7775 - val_loss: 15.8314 - val_mean_absolute_error: 3.3245 - 30ms/epoch - 5ms/step
## Epoch 72/100
## 6/6 - 0s - loss: 46.2637 - mean_absolute_error: 4.8777 - val_loss: 14.4350 - val_mean_absolute_error: 3.1350 - 46ms/epoch - 8ms/step
## Epoch 73/100
## 6/6 - 0s - loss: 42.7639 - mean_absolute_error: 4.9785 - val_loss: 14.7951 - val_mean_absolute_error: 3.1797 - 37ms/epoch - 6ms/step
## Epoch 74/100
## 6/6 - 0s - loss: 41.9135 - mean_absolute_error: 4.8354 - val_loss: 15.1695 - val_mean_absolute_error: 3.2331 - 34ms/epoch - 6ms/step
## Epoch 75/100
## 6/6 - 0s - loss: 44.9491 - mean_absolute_error: 4.9292 - val_loss: 14.3676 - val_mean_absolute_error: 3.1232 - 34ms/epoch - 6ms/step
## Epoch 76/100
## 6/6 - 0s - loss: 46.2250 - mean_absolute_error: 4.9832 - val_loss: 14.7970 - val_mean_absolute_error: 3.1938 - 30ms/epoch - 5ms/step
## Epoch 77/100
## 6/6 - 0s - loss: 41.5583 - mean_absolute_error: 4.7318 - val_loss: 13.7038 - val_mean_absolute_error: 2.9800 - 30ms/epoch - 5ms/step
## Epoch 78/100
## 6/6 - 0s - loss: 45.5637 - mean_absolute_error: 5.0121 - val_loss: 13.6442 - val_mean_absolute_error: 2.9538 - 31ms/epoch - 5ms/step
## Epoch 79/100
## 6/6 - 0s - loss: 42.1623 - mean_absolute_error: 4.8332 - val_loss: 13.5154 - val_mean_absolute_error: 2.9535 - 30ms/epoch - 5ms/step
## Epoch 80/100
## 6/6 - 0s - loss: 35.3987 - mean_absolute_error: 4.4426 - val_loss: 13.6741 - val_mean_absolute_error: 2.9704 - 29ms/epoch - 5ms/step
## Epoch 81/100
## 6/6 - 0s - loss: 42.9012 - mean_absolute_error: 4.8859 - val_loss: 13.9039 - val_mean_absolute_error: 3.0218 - 30ms/epoch - 5ms/step
## Epoch 82/100
## 6/6 - 0s - loss: 45.3977 - mean_absolute_error: 4.9875 - val_loss: 13.7371 - val_mean_absolute_error: 3.0010 - 30ms/epoch - 5ms/step
## Epoch 83/100
## 6/6 - 0s - loss: 40.1978 - mean_absolute_error: 4.5387 - val_loss: 13.5906 - val_mean_absolute_error: 2.9698 - 29ms/epoch - 5ms/step
## Epoch 84/100
## 6/6 - 0s - loss: 42.1860 - mean_absolute_error: 4.7813 - val_loss: 13.6459 - val_mean_absolute_error: 2.9477 - 27ms/epoch - 5ms/step
## Epoch 85/100
## 6/6 - 0s - loss: 38.7609 - mean_absolute_error: 4.6478 - val_loss: 13.6111 - val_mean_absolute_error: 2.9239 - 29ms/epoch - 5ms/step
## Epoch 86/100
## 6/6 - 0s - loss: 38.5731 - mean_absolute_error: 4.6000 - val_loss: 13.2965 - val_mean_absolute_error: 2.9083 - 29ms/epoch - 5ms/step
## Epoch 87/100
## 6/6 - 0s - loss: 42.2428 - mean_absolute_error: 4.6528 - val_loss: 13.2875 - val_mean_absolute_error: 2.9479 - 30ms/epoch - 5ms/step
## Epoch 88/100
## 6/6 - 0s - loss: 40.4984 - mean_absolute_error: 4.6650 - val_loss: 13.0986 - val_mean_absolute_error: 2.9105 - 38ms/epoch - 6ms/step
## Epoch 89/100
## 6/6 - 0s - loss: 42.3555 - mean_absolute_error: 4.7697 - val_loss: 13.3123 - val_mean_absolute_error: 2.9625 - 29ms/epoch - 5ms/step
## Epoch 90/100
## 6/6 - 0s - loss: 36.8049 - mean_absolute_error: 4.5736 - val_loss: 12.8433 - val_mean_absolute_error: 2.8263 - 27ms/epoch - 5ms/step
## Epoch 91/100
## 6/6 - 0s - loss: 42.8140 - mean_absolute_error: 4.6692 - val_loss: 12.9752 - val_mean_absolute_error: 2.9151 - 31ms/epoch - 5ms/step
## Epoch 92/100
## 6/6 - 0s - loss: 39.4167 - mean_absolute_error: 4.6356 - val_loss: 12.9761 - val_mean_absolute_error: 2.8851 - 31ms/epoch - 5ms/step
## Epoch 93/100
## 6/6 - 0s - loss: 37.2282 - mean_absolute_error: 4.6057 - val_loss: 12.8412 - val_mean_absolute_error: 2.8146 - 31ms/epoch - 5ms/step
## Epoch 94/100
## 6/6 - 0s - loss: 39.9037 - mean_absolute_error: 4.5760 - val_loss: 13.1590 - val_mean_absolute_error: 2.8801 - 32ms/epoch - 5ms/step
## Epoch 95/100
## 6/6 - 0s - loss: 38.1198 - mean_absolute_error: 4.6399 - val_loss: 13.3037 - val_mean_absolute_error: 2.8741 - 33ms/epoch - 6ms/step
## Epoch 96/100
## 6/6 - 0s - loss: 41.1695 - mean_absolute_error: 4.7062 - val_loss: 13.4858 - val_mean_absolute_error: 2.9030 - 43ms/epoch - 7ms/step
## Epoch 97/100
## 6/6 - 0s - loss: 37.2533 - mean_absolute_error: 4.3722 - val_loss: 12.9690 - val_mean_absolute_error: 2.8245 - 34ms/epoch - 6ms/step
## Epoch 98/100
## 6/6 - 0s - loss: 38.8862 - mean_absolute_error: 4.6539 - val_loss: 12.9727 - val_mean_absolute_error: 2.8281 - 35ms/epoch - 6ms/step

c(loss, mae) %<-% (model %>% evaluate(x_test, y_test, verbose = 0))
paste0("Mean absolute error on test set: ", sprintf("%.2f", mae))

## [1] "Mean absolute error on test set: 2.62"

3.2.8 Plot the training process

plot(history)

### Calculating the predicted values on test data

pred2 <- model %>% 
  predict(x_test) %>% k_get_value()

head(cbind(pred2,y_test))

##               y_test
## [1,] 23.87188   21.6
## [2,] 32.19261   33.4
## [3,] 31.18039   36.2
## [4,] 14.50413   27.1
## [5,] 14.90367   15.0
## [6,] 17.18917   19.9

• calculating mean absolute error and root mean square error and ploting

error <- y_test-pred2
head(error)

##             [,1]
## [1,] -2.27187767
## [2,]  1.20738831
## [3,]  5.01961060
## [4,] 12.59587059
## [5,]  0.09632874
## [6,]  2.71082726

rmse <- sqrt(mean(error)^2)
rmse

## [1] 0.3127118

plot(error)

3.3 Convolutional neural netwrok

3.3.1 Import library

library(keras)

3.3.2 Importing the data

mnist <- dataset_mnist()

• mnist is list; it contains trainx, trainy, testx, testy

class(mnist)

## [1] "list"

• the dim of “mnist$train$x” is 60000 28 28

# head(mnist)

3.3.3 preparing the data

• randomly sampling 1000 cases for training and 100 for testing

set.seed(123)
index <- sample(nrow(mnist$train$x), 1000)
x_train <- mnist$train$x[index,,]
y_train <- (mnist$train$y[index])

index <- sample(nrow(mnist$test$x), 100)
x_test <- mnist$test$x[index,,]
y_test <- (mnist$test$y[index])

• dim of four data sets

dim(x_train)

## [1] 1000   28   28

dim(y_train)

## [1] 1000

dim(x_test)

## [1] 100  28  28

dim(y_test)

## [1] 100

3.3.3.1 Generate tensors

• each image is 28*28 pixel size; pass these values to computer

img_rows <- 28
img_cols <- 28

• using array_reshape() function to transform list data into tensors

x_train <- array_reshape(x_train,
                         c(nrow(x_train),
                           img_rows,
                           img_cols, 1))
x_test <- array_reshape(x_test,
                        c(nrow(x_test),
                          img_rows,
                          img_cols, 1))
input_shape <- c(img_rows,
                 img_cols, 1)

• this below is tensor data

dim(x_train)

## [1] 1000   28   28    1

3.3.3.2 Normalization and one-hot-encoded (dummy)

• training (features) data is rescaled by dividing the maxmimum to be normalized

x_train <- x_train / 255
x_test <- x_test / 255

• converse targets into one-hot-encoded (dummy) type using to_categorical() function

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

y_train[1,]

##  [1] 0 0 0 0 0 0 1 0 0 0

3.3.4 Creating the model

model <- keras_model_sequential() %>%
  layer_conv_2d(filters = 32,
                kernel_size = c(3,3),
                activation = 'relu',
                input_shape = input_shape) %>% 
  
  layer_conv_2d(filters = 64,
                kernel_size = c(3,3),
                activation = 'relu') %>% 
  
  layer_max_pooling_2d(pool_size = c(2, 2)) %>% 
  
  layer_dropout(rate = 0.25) %>% 
  
  layer_flatten() %>% 
  layer_dense(units = 128,
              activation = 'relu') %>% 
  
  layer_dropout(rate = 0.5) %>% 
  layer_dense(units = num_classes,
              activation = 'softmax')

• summary of model

model %>% summary()

## Model: "sequential_2"
## ________________________________________________________________________________
##  Layer (type)                       Output Shape                    Param #     
## ================================================================================
##  conv2d_1 (Conv2D)                  (None, 26, 26, 32)              320         
##  conv2d (Conv2D)                    (None, 24, 24, 64)              18496       
##  max_pooling2d (MaxPooling2D)       (None, 12, 12, 64)              0           
##  dropout_4 (Dropout)                (None, 12, 12, 64)              0           
##  flatten (Flatten)                  (None, 9216)                    0           
##  dense_5 (Dense)                    (None, 128)                     1179776     
##  dropout_3 (Dropout)                (None, 128)                     0           
##  dense_4 (Dense)                    (None, 10)                      1290        
## ================================================================================
## Total params: 1,199,882
## Trainable params: 1,199,882
## Non-trainable params: 0
## ________________________________________________________________________________

3.3.4.1 compiling

• loss function is categorical crossentropy; the gradient descent will be optimized by adadelta;

model %>% compile(
  loss = loss_categorical_crossentropy,
  optimizer = optimizer_adadelta(),
  metrics = c('accuracy')
)

3.3.5 Training

batch_size <- 128
epochs <- 10

# Train model
history <- model %>% fit(
  x_train, y_train,
  batch_size = batch_size,
  epochs = epochs,
  validation_split = 0.2
)

## Epoch 1/10
## 
## 1/7 [===>..........................] - ETA: 3s - loss: 2.3147 - accuracy: 0.0859
## 2/7 [=======>......................] - ETA: 0s - loss: 2.3193 - accuracy: 0.0820
## 3/7 [===========>..................] - ETA: 0s - loss: 2.3129 - accuracy: 0.0885
## 4/7 [================>.............] - ETA: 0s - loss: 2.3146 - accuracy: 0.0938
## 5/7 [====================>.........] - ETA: 0s - loss: 2.3149 - accuracy: 0.0984
## 6/7 [========================>.....] - ETA: 0s - loss: 2.3147 - accuracy: 0.0951
## 7/7 [==============================] - 2s 145ms/step - loss: 2.3146 - accuracy: 0.0938 - val_loss: 2.3096 - val_accuracy: 0.0900
## Epoch 2/10
## 
## 1/7 [===>..........................] - ETA: 0s - loss: 2.2889 - accuracy: 0.1797
## 2/7 [=======>......................] - ETA: 0s - loss: 2.3096 - accuracy: 0.1172
## 3/7 [===========>..................] - ETA: 0s - loss: 2.3061 - accuracy: 0.1172
## 4/7 [================>.............] - ETA: 0s - loss: 2.3120 - accuracy: 0.1074
## 5/7 [====================>.........] - ETA: 0s - loss: 2.3144 - accuracy: 0.1016
## 6/7 [========================>.....] - ETA: 0s - loss: 2.3142 - accuracy: 0.1003
## 7/7 [==============================] - 1s 128ms/step - loss: 2.3139 - accuracy: 0.1000 - val_loss: 2.3086 - val_accuracy: 0.0900
## Epoch 3/10
## 
## 1/7 [===>..........................] - ETA: 0s - loss: 2.3111 - accuracy: 0.0859
## 2/7 [=======>......................] - ETA: 0s - loss: 2.3072 - accuracy: 0.1094
## 3/7 [===========>..................] - ETA: 0s - loss: 2.3127 - accuracy: 0.0990
## 4/7 [================>.............] - ETA: 0s - loss: 2.3103 - accuracy: 0.1035
## 5/7 [====================>.........] - ETA: 0s - loss: 2.3102 - accuracy: 0.1016
## 6/7 [========================>.....] - ETA: 0s - loss: 2.3094 - accuracy: 0.1016
## 7/7 [==============================] - 1s 166ms/step - loss: 2.3105 - accuracy: 0.0988 - val_loss: 2.3075 - val_accuracy: 0.0950
## Epoch 4/10
## 
## 1/7 [===>..........................] - ETA: 0s - loss: 2.2972 - accuracy: 0.1016
## 2/7 [=======>......................] - ETA: 0s - loss: 2.3120 - accuracy: 0.0781
## 3/7 [===========>..................] - ETA: 0s - loss: 2.3166 - accuracy: 0.0859
## 4/7 [================>.............] - ETA: 0s - loss: 2.3148 - accuracy: 0.0879
## 5/7 [====================>.........] - ETA: 0s - loss: 2.3147 - accuracy: 0.1016
## 6/7 [========================>.....] - ETA: 0s - loss: 2.3135 - accuracy: 0.1029
## 7/7 [==============================] - 1s 128ms/step - loss: 2.3138 - accuracy: 0.1013 - val_loss: 2.3066 - val_accuracy: 0.1050
## Epoch 5/10
## 
## 1/7 [===>..........................] - ETA: 0s - loss: 2.3250 - accuracy: 0.0859
## 2/7 [=======>......................] - ETA: 0s - loss: 2.3154 - accuracy: 0.1016
## 3/7 [===========>..................] - ETA: 0s - loss: 2.3104 - accuracy: 0.1094
## 4/7 [================>.............] - ETA: 0s - loss: 2.3127 - accuracy: 0.1113
## 5/7 [====================>.........] - ETA: 0s - loss: 2.3111 - accuracy: 0.1078
## 6/7 [========================>.....] - ETA: 0s - loss: 2.3098 - accuracy: 0.1133
## 7/7 [==============================] - 1s 119ms/step - loss: 2.3103 - accuracy: 0.1138 - val_loss: 2.3055 - val_accuracy: 0.1050
## Epoch 6/10
## 
## 1/7 [===>..........................] - ETA: 0s - loss: 2.3161 - accuracy: 0.0703
## 2/7 [=======>......................] - ETA: 0s - loss: 2.3192 - accuracy: 0.0938
## 3/7 [===========>..................] - ETA: 0s - loss: 2.3188 - accuracy: 0.0859
## 4/7 [================>.............] - ETA: 0s - loss: 2.3124 - accuracy: 0.1133
## 5/7 [====================>.........] - ETA: 0s - loss: 2.3090 - accuracy: 0.1094
## 6/7 [========================>.....] - ETA: 0s - loss: 2.3093 - accuracy: 0.1120
## 7/7 [==============================] - 1s 114ms/step - loss: 2.3105 - accuracy: 0.1100 - val_loss: 2.3044 - val_accuracy: 0.1050
## Epoch 7/10
## 
## 1/7 [===>..........................] - ETA: 0s - loss: 2.2928 - accuracy: 0.1250
## 2/7 [=======>......................] - ETA: 0s - loss: 2.3015 - accuracy: 0.0938
## 3/7 [===========>..................] - ETA: 0s - loss: 2.3058 - accuracy: 0.0885
## 4/7 [================>.............] - ETA: 0s - loss: 2.3050 - accuracy: 0.0938
## 5/7 [====================>.........] - ETA: 0s - loss: 2.3031 - accuracy: 0.1000
## 6/7 [========================>.....] - ETA: 0s - loss: 2.3046 - accuracy: 0.0951
## 7/7 [==============================] - 1s 113ms/step - loss: 2.3035 - accuracy: 0.0988 - val_loss: 2.3035 - val_accuracy: 0.1050
## Epoch 8/10
## 
## 1/7 [===>..........................] - ETA: 0s - loss: 2.3094 - accuracy: 0.0781
## 2/7 [=======>......................] - ETA: 0s - loss: 2.3053 - accuracy: 0.0938
## 3/7 [===========>..................] - ETA: 0s - loss: 2.3104 - accuracy: 0.0990
## 4/7 [================>.............] - ETA: 0s - loss: 2.3083 - accuracy: 0.0918
## 5/7 [====================>.........] - ETA: 0s - loss: 2.3072 - accuracy: 0.0922
## 6/7 [========================>.....] - ETA: 0s - loss: 2.3037 - accuracy: 0.1068
## 7/7 [==============================] - 1s 113ms/step - loss: 2.3028 - accuracy: 0.1050 - val_loss: 2.3026 - val_accuracy: 0.1050
## Epoch 9/10
## 
## 1/7 [===>..........................] - ETA: 0s - loss: 2.2924 - accuracy: 0.1094
## 2/7 [=======>......................] - ETA: 0s - loss: 2.2931 - accuracy: 0.1172
## 3/7 [===========>..................] - ETA: 0s - loss: 2.3012 - accuracy: 0.1172
## 4/7 [================>.............] - ETA: 0s - loss: 2.3016 - accuracy: 0.1094
## 5/7 [====================>.........] - ETA: 0s - loss: 2.3045 - accuracy: 0.1031
## 6/7 [========================>.....] - ETA: 0s - loss: 2.3075 - accuracy: 0.0990
## 7/7 [==============================] - 1s 109ms/step - loss: 2.3079 - accuracy: 0.1000 - val_loss: 2.3016 - val_accuracy: 0.1050
## Epoch 10/10
## 
## 1/7 [===>..........................] - ETA: 0s - loss: 2.3022 - accuracy: 0.1094
## 2/7 [=======>......................] - ETA: 0s - loss: 2.3064 - accuracy: 0.1016
## 3/7 [===========>..................] - ETA: 0s - loss: 2.3089 - accuracy: 0.1016
## 4/7 [================>.............] - ETA: 0s - loss: 2.3101 - accuracy: 0.1055
## 5/7 [====================>.........] - ETA: 0s - loss: 2.3126 - accuracy: 0.1016
## 6/7 [========================>.....] - ETA: 0s - loss: 2.3127 - accuracy: 0.0990
## 7/7 [==============================] - 1s 107ms/step - loss: 2.3124 - accuracy: 0.1025 - val_loss: 2.3006 - val_accuracy: 0.1050

plot(history)

3.3.6 Evaluating the accuracy

score <- model %>% evaluate(x_test,
                            y_test)

## 
## 1/4 [======>.......................] - ETA: 0s - loss: 2.3083 - accuracy: 0.0938
## 4/4 [==============================] - 0s 6ms/step - loss: 2.2909 - accuracy: 0.1300

score

##     loss accuracy 
## 2.290876 0.130000