In the previous post I fitted a neural network to the cars_19 dataset using the neuralnet package.  In this post I am going to use TensorFlow to fit a deep neural network using the same data.

The main difference between the neuralnet package and TensorFlow is TensorFlow uses the adagrad optimizer by default whereas neuralnet uses rprop+  Adagrad is a modified stochastic gradient descent optimizer with a per-parameter learning rate.

The data which is all 2019 vehicles which are non pure electric (1253 vehicles) are summarized in previous posts below.

str(cars_19)
'data.frame':    1253 obs. of  12 variables:
 $ fuel_economy_combined: int  21 28 21 26 28 11 15 18 17 15 ...
 $ eng_disp             : num  3.5 1.8 4 2 2 8 6.2 6.2 6.2 6.2 ...
 $ num_cyl              : int  6 4 8 4 4 16 8 8 8 8 ...
 $ transmission         : Factor w/ 7 levels "A","AM","AMS",..: 3 2 6 3 6 3 6 6 6 5 ...
 $ num_gears            : int  9 6 8 7 8 7 8 8 8 7 ...
 $ air_aspired_method   : Factor w/ 5 levels "Naturally Aspirated",..: 4 4 4 4 4 4 3 1 3 3 ...
 $ regen_brake          : Factor w/ 3 levels "","Electrical Regen Brake",..: 2 1 1 1 1 1 1 1 1 1 ...
 $ batt_capacity_ah     : num  4.25 0 0 0 0 0 0 0 0 0 ...
 $ drive                : Factor w/ 5 levels "2-Wheel Drive, Front",..: 4 2 2 4 2 4 2 2 2 2 ...
 $ fuel_type            : Factor w/ 5 levels "Diesel, ultra low sulfur (15 ppm, maximum)",..: 4 3 3 5 3 4 4 4 4 4 ...
 $ cyl_deactivate       : Factor w/ 2 levels "N","Y": 1 1 1 1 1 2 1 2 2 1 ...
 $ variable_valve       : Factor w/ 2 levels "N","Y": 2 2 2 2 2 2 2 2 2 2 ...

To prepare the data to fit the neural network, TensorFlow requires categorical variables to be converted into a dense representation by using the column_embedding() function.

cols <- feature_columns(
  column_numeric(colnames(cars_19[c(2, 3, 5, 8)])),
  column_embedding(column_categorical_with_identity("transmission", num_buckets = 7),dimension = 1),
  column_embedding(column_categorical_with_identity("air_aspired_method", num_buckets = 5),dimension=1),
  column_embedding(column_categorical_with_identity("regen_brake", num_buckets = 3),dimension=1),
  column_embedding(column_categorical_with_identity("drive", num_buckets = 5),dimension=1),
  column_embedding(column_categorical_with_identity("fuel_type", num_buckets = 5),dimension=1),
  column_embedding(column_categorical_with_identity("cyl_deactivate", num_buckets = 2),dimension=1),
  column_embedding(column_categorical_with_identity("variable_valve", num_buckets = 2),dimension=1)
)

Similar to the neural network I fitted using neuralnet(), I am going to use two hidden layers with seven and three neurons respectively.

Train, evaluate, and predict:

#Create a deep neural network (DNN) estimator.
model <- dnn_regressor(hidden_units=c(7,3),feature_columns = cols)

set.seed(123)
indices <- sample(1:nrow(cars_19), size = 0.75 * nrow(cars_19))
train <- cars_19[indices, ]
test <- cars_19[-indices, ]

#train model
model %>% train(cars_19_input_fn(train, num_epochs = 1000))

#evaluate model
model %>% evaluate(cars_19_input_fn(test))

#predict
yhat <- model %>% predict(cars_19_input_fn(test))

yhat <- unlist(yhat)
y <- test$fuel_economy_combined

postResample(yhat, y)
RMSE  Rsquared       MAE 
1.9640173 0.8700275 1.4838347 

The results are similar to the other models and neuralnet().

I am going to look at the error rate in TensorBoard which is a visualization tool.  TensorBoard is great for visualizing TensorFlow graphs and for plotting quantitative metrics about the execution of the graph.  Below is the mean squared error at each iteration.  It stabilizes fairly quickly.  Next post I will get into TensorBoard in a lot more depth.