Data Science, Machine Learning and Predictive Analytics: November 2020

In the previous posts, I used popular machine learning algorithms to fit models to best predict MPG using the cars_19 dataset. It was discovered that support vector machine produced the lowest RMSE. In this post I am going to use XGBoost to build a predictive model and compare the RMSE to the other models.

The raw data is located on the EPA government site.

Similar to the other models, the variables/features I am using are: Engine displacement (size), number of cylinders, transmission type, number of gears, air inspired method, regenerative braking type, battery capacity Ah, drivetrain, fuel type, cylinder deactivate, and variable valve. Unlike the other models, the XGBoost package does not handle factors so I will have to transform them into dummy variables. After creating the dummy variables, I will be using 33 input variables.

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 ...

After getting a working model and performing trial and error exploratory analysis to estimate the eta and tree depth hyperparameters, I am going to run a grid search. I am going to run 64 XGBoost models

#create hyperparameter grid
hyper_grid <- expand.grid(max_depth = seq(3, 6, 1), eta = seq(.2, .35, .01))

Using a for loop and a 5 fold CV

for (j in 1:nrow(hyper_grid)) {
  set.seed(123)
  m_xgb_untuned <- xgb.cv(
    data = train[, 2:34],
    label = train[, 1],
    nrounds = 1000,
    objective = "reg:squarederror",
    early_stopping_rounds = 3,
    nfold = 5,
    max_depth = hyper_grid$max_depth[j],
    eta = hyper_grid$eta[j]
  )
  
  xgb_train_rmse[j] <- m_xgb_untuned$evaluation_log$train_rmse_mean[m_xgb_untuned$best_iteration]
  xgb_test_rmse[j] <- m_xgb_untuned$evaluation_log$test_rmse_mean[m_xgb_untuned$best_iteration]
  
  cat(j, "\n")
}

ETA of .25 and max tree depth of 6 produces the model with the lowest test RMSE

I am going to run this combination below:

m1_xgb <-
  xgboost(
    data = train[, 2:34],
    label = train[, 1],
    nrounds = 1000,
    objective = "reg:squarederror",
    early_stopping_rounds = 3,
    max_depth = 6,
    eta = .25
  )

RMSE      Rsquared   MAE
1.7374    0.8998     1.231

Graph of features that are most explanatory:

Graph of first 3 trees:

Residuals:

Fit:

Comparison of RMSE:

svm = .93
XGBoost = 1.74
gradient boosting = 1.8
random forest = 1.9
neural network = 2.06
decision tree = 2.49
mlr = 2.6

R XGBoost Regression