15.3 Model Training Process

  1. Train each base model using the same seed (seed = 123), fold assignment (fold_assignment = "Modulo") and saving the cross-validated predictions (keep_cross_validation_predictions = TRUE).
# Regularized regression base learner
best_glm <- h2o.glm(
  x = X,
  y = Y,
  training_frame = train_h2o,
  alpha = 0.1,
  remove_collinear_columns = TRUE,
  nfolds = 10,
  fold_assignment = "Modulo",
  keep_cross_validation_predictions = TRUE,
  seed = 123
)
## 
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# Random forest base learner
best_rf <- h2o.randomForest(
  x = X,
  y = Y,
  training_frame = train_h2o,
  ntrees = 1000,
  mtries = 20,
  max_depth = 30,
  min_rows = 1,
  sample_rate = 0.8,
  nfolds = 10,
  fold_assignment = "Modulo",
  keep_cross_validation_predictions = TRUE,
  seed = 123,
  stopping_rounds = 50,
  stopping_metric = "RMSE",
  stopping_tolerance = 0
)
## Warning in .h2o.processResponseWarnings(res): early stopping is enabled but neither score_tree_interval or score_each_iteration are defined. Early stopping will not be reproducible!.
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# GBM base learner
best_gbm <- h2o.gbm(
  x = X,
  y = Y,
  training_frame = train_h2o,
  ntrees = 5000,
  learn_rate = 0.01,
  max_depth = 7,
  min_rows = 5,
  sample_rate = 0.8,
  nfolds = 10,
  fold_assignment = "Modulo",
  keep_cross_validation_predictions = TRUE,
  seed = 123,
  stopping_rounds = 50,
  stopping_metric = "RMSE",
  stopping_tolerance = 0
)
## Warning in .h2o.processResponseWarnings(res): early stopping is enabled but neither score_tree_interval or score_each_iteration are defined. Early stopping will not be reproducible!.
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# XGBoost base learner
#   We cannot run this under Windows
  1. Set up the ensemble by
  • Defining a list \(L\) of tuned based learners
  • Defining a metalearner algorithm
# Stacked model
ensemble_tree <- h2o.stackedEnsemble(
  x = X,
  y = Y,
  training_frame = train_h2o,
  model_id = "my_tree_ensemble",
  base_models = list(best_glm, best_rf, best_gbm),
  # Meta learner: random forest
  metalearner_algorithm = "drf"
)
  1. Explore models correlations
ModelList <- list(
  glm = best_glm,
  rf = best_rf,
  gbm = best_gbm
)

extract_cv <- function(x){
  x@model$cross_validation_holdout_predictions_frame_id$name |>
    h2o.getFrame() |>
    as.vector()
}

lapply(ModelList, extract_cv) |>
  as.data.frame() |>
  cor()
##           glm        rf       gbm
## glm 1.0000000 0.9421599 0.9346891
## rf  0.9421599 1.0000000 0.9919788
## gbm 0.9346891 0.9919788 1.0000000

As we can see the models show very similar results, so this case isn’t the best one to perform a stacking model.

  1. Comparing model performance
# Defining the rmse function
get_rmse <- function(model) {
  results <- h2o.performance(model, newdata = test_h2o)
  results@metrics$RMSE
}

# Get results from base learners
BaseLearnersRmse <- sapply(ModelList, get_rmse)
BaseLearnersRmse
##      glm       rf      gbm 
## 30018.69 22247.60 20105.70
# Stacked results
StackRmse <- get_rmse(ensemble_tree)
StackRmse
## [1] 21300.69
# Ratio
StackRmse/BaseLearnersRmse
##       glm        rf       gbm 
## 0.7095810 0.9574378 1.0594352