R: Gradient Boosted Machine to Predict MPG for 2019 Vehicles

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Continuing on the below post, I am going to use a gradient boosted machine model to predict combined miles per gallon for all 2019 motor vehicles.

Part 1: Using Decision Trees and Random Forest to Predict MPG for 2019 Vehicles

The raw data is located on the EPA government site

The variables/features I am using for the models 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. 

There are 1253 vehicles in the dataset (does not include pure electric vehicles) summarized below.

fuel_economy_combined    eng_disp        num_cyl       transmission<br /> Min.   :11.00         Min.   :1.000   Min.   : 3.000   A  :301     <br /> 1st Qu.:19.00         1st Qu.:2.000   1st Qu.: 4.000   AM : 46     <br /> Median :23.00         Median :3.000   Median : 6.000   AMS: 87     <br /> Mean   :23.32         Mean   :3.063   Mean   : 5.533   CVT: 50     <br /> 3rd Qu.:26.00         3rd Qu.:3.600   3rd Qu.: 6.000   M  :148     <br /> Max.   :58.00         Max.   :8.000   Max.   :16.000   SA :555     <br />                                                        SCV: 66     <br />   num_gears                      air_aspired_method<br /> Min.   : 1.000   Naturally Aspirated      :523     <br /> 1st Qu.: 6.000   Other                    :  5     <br /> Median : 7.000   Supercharged             : 55     <br /> Mean   : 7.111   Turbocharged             :663     <br /> 3rd Qu.: 8.000   Turbocharged+Supercharged:  7     <br /> Max.   :10.000                                     <br />                                                    <br />                 regen_brake   batt_capacity_ah <br />             No        :1194   Min.   : 0.0000  <br /> Electrical Regen Brake:  57   1st Qu.: 0.0000  <br /> Hydraulic Regen Brake :   2   Median : 0.0000  <br />                               Mean   : 0.3618  <br />                               3rd Qu.: 0.0000  <br />                               Max.   :20.0000  <br />                                                <br />                     drive    cyl_deactivate<br /> 2-Wheel Drive, Front   :345  Y: 172<br /> 2-Wheel Drive, Rear    :345  N:1081<br /> 4-Wheel Drive          :174  <br /> All Wheel Drive        :349  <br /> Part-time 4-Wheel Drive: 40  <br />                              <br />                              <br />                                      fuel_type   <br /> Diesel, ultra low sulfur (15 ppm, maximum): 28           <br /> Gasoline (Mid Grade Unleaded Recommended) : 16           <br /> Gasoline (Premium Unleaded Recommended)   :298                 <br /> Gasoline (Premium Unleaded Required)      :320                 <br /> Gasoline (Regular Unleaded Recommended)   :591                 <br />                                                                <br />                                                                <br /> variable_valve<br /> N:  38        <br /> Y:1215        <br />

Starting with an untuned base model:

trees <- 1200<br />m_boosted_reg_untuned <- gbm(<br />  formula = fuel_economy_combined ~ .,<br />  data    = train,<br />  n.trees = trees,<br />  distribution = "gaussian"<br />)<br />

> summary(m_boosted_reg_untuned)<br />                                  var     rel.inf<br />eng_disp                     eng_disp 41.26273684<br />batt_capacity_ah     batt_capacity_ah 24.53458898<br />transmission             transmission 11.33253784<br />drive                           drive  8.59300859<br />regen_brake               regen_brake  8.17877824<br />air_aspired_method air_aspired_method  2.11397865<br />num_gears                   num_gears  1.90999021<br />fuel_type                   fuel_type  1.65692562<br />num_cyl                       num_cyl  0.22260369<br />variable_valve         variable_valve  0.11043532<br />cyl_deactivate         cyl_deactivate  0.08441602<br />> boosted_stats_untuned<br />     RMSE  Rsquared       MAE <br />2.4262643 0.8350367 1.7513331 <br />

The untuned GBM model performs better than the multiple linear regression model, but worse than the random forest.

I am going to tune the GBM by running a grid search:

#create hyperparameter grid<br />hyper_grid <- expand.grid(<br />  shrinkage = seq(.07, .12, .01),<br />  interaction.depth = 1:7,<br />  optimal_trees = 0,<br />  min_RMSE = 0<br />)<br /><br />#grid search<br />for (i in 1:nrow(hyper_grid)) {<br />  set.seed(123)<br />  gbm.tune <- gbm(<br />    formula = fuel_economy_combined ~ .,<br />    data = train_random,<br />    distribution = "gaussian",<br />    n.trees = 5000,<br />    interaction.depth = hyper_grid$interaction.depth[i],<br />    shrinkage = hyper_grid$shrinkage[i],<br />  )<br />  <br />  hyper_grid$optimal_trees[i] <- which.min(gbm.tune$train.error)<br />  hyper_grid$min_RMSE[i] <- sqrt(min(gbm.tune$train.error))<br />  <br />  cat(i, "\n")<br />}<br />

The hyper grid is 42 rows which is all combinations of shrinkage and interaction depths specified above.

> head(hyper_grid)<br />  shrinkage interaction.depth optimal_trees min_RMSE<br />1      0.07                 1             0        0<br />2      0.08                 1             0        0<br />3      0.09                 1             0        0<br />4      0.10                 1             0        0<br />5      0.11                 1             0        0<br />6      0.12                 1             0        0

After running the grid search, it is apparent that there is overfitting. This is something to be very careful about.  I am going to run a 5 fold cross validation to estimate out of bag error vs MSE.  After running the 5 fold CV, this is the best model that does not overfit:

> m_boosted_reg <- gbm(<br />  formula = fuel_economy_combined ~ .,<br />  data    = train,<br />  n.trees = trees,<br />  distribution = "gaussian",<br />  shrinkage = .09,<br />  cv.folds = 5,<br />  interaction.depth = 5<br />)<br /><br />best.iter <- gbm.perf(m_boosted_reg, method = "cv")<br />pred_boosted_reg_ <- predict(m_boosted_reg,n.trees=1183, newdata = test)<br />mse_boosted_reg_ <- RMSE(pred = pred_boosted_reg, obs = test$fuel_economy_combined) ^2<br />boosted_stats<-postResample(pred_boosted_reg,test$fuel_economy_combined)<br />

The fitted black curve above is MSE and the fitted green curve is the out of bag estimated error.  1183 is the optimal amount of iterations.

> pred_boosted_reg <- predict(m_boosted_reg,n.trees=1183, newdata = test)<br />> mse_boosted_reg <- RMSE(pred = pred_boosted_reg, obs = test$fuel_economy_combined) ^2<br />> boosted_stats<-postResample(pred_boosted_reg,test$fuel_economy_combined)<br />> boosted_stats<br />     RMSE  Rsquared       MAE <br />1.8018793 0.9092727 1.3334459 <br />> mse_boosted_reg<br />3.246769 <br />

The tuned gradient boosted model performs better than the random forest with a MSE of 3.25 vs 3.67 for the random forest.

> summary(res)<br />    Min.  1st Qu.   Median     Mean  3rd Qu.     Max. <br />-5.40000 -0.90000  0.00000  0.07643  1.10000  9.10000 <br />

50% of the predictions are within 1 MPG of the EPA Government Estimate.

The largest residuals are exotics and a hybrid which are the more unique data points in the dataset. 

> tmp[which(abs(res) > boosted_stats[1] * 3), ] <br />                  Division            Carline fuel_economy_combined pred_boosted_reg<br />642  HYUNDAI MOTOR COMPANY         Ioniq Blue                    58             48.5<br />482 KIA MOTORS CORPORATION           Forte FE                    35             28.7<br />39             Lamborghini    Aventador Coupe                    11             17.2<br />40             Lamborghini Aventador Roadster                    11             17.2<br />

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