rpart: Regression

    # nolint start
    library(mlexperiments)

See https://github.com/kapsner/mlexperiments/blob/main/R/learner_rpart.R for implementation details.

# Preprocessing

## Import and Prepare Data

    library(mlbench)
    data("BostonHousing")
    dataset <- BostonHousing |>
      data.table::as.data.table() |>
      na.omit()

    feature_cols <- colnames(dataset)[1:13]
    target_col <- "medv"
    cat_vars <- "chas"

## General Configurations

    seed <- 123
    if (isTRUE(as.logical(Sys.getenv("_R_CHECK_LIMIT_CORES_")))) {
      # on cran
      ncores <- 2L
    } else {
      ncores <- ifelse(
        test = parallel::detectCores() > 4,
        yes = 4L,
        no = ifelse(
          test = parallel::detectCores() < 2L,
          yes = 1L,
          no = parallel::detectCores()
        )
      )
    }
    options("mlexperiments.bayesian.max_init" = 4L)

## Generate Training- and Test Data

    data_split <- splitTools::partition(
      y = dataset[, get(target_col)],
      p = c(train = 0.7, test = 0.3),
      type = "stratified",
      seed = seed
    )

    train_x <- data.matrix(
      dataset[data_split$train, .SD, .SDcols = feature_cols]
    )
    train_y <- dataset[data_split$train, get(target_col)]

    test_x <- data.matrix(
      dataset[data_split$test, .SD, .SDcols = feature_cols]
    )
    test_y <- dataset[data_split$test, get(target_col)]

## Generate Training Data Folds

    fold_list <- splitTools::create_folds(
      y = train_y,
      k = 3,
      type = "stratified",
      seed = seed
    )

# Experiments

## Prepare Experiments

    # required learner arguments, not optimized
    learner_args <- list(method = "anova")

    # set arguments for predict function and performance metric,
    # required for mlexperiments::MLCrossValidation and
    # mlexperiments::MLNestedCV
    predict_args <- list(type = "vector")
    performance_metric <- metric("MSE")
    performance_metric_args <- NULL
    return_models <- FALSE

    # required for grid search and initialization of bayesian optimization
    parameter_grid <- expand.grid(
      minsplit = seq(2L, 82L, 10L),
      cp = seq(0.01, 0.1, 0.01),
      maxdepth = seq(2L, 30L, 5L)
    )
    # reduce to a maximum of 10 rows
    if (nrow(parameter_grid) > 10) {
      set.seed(123)
      sample_rows <- sample(seq_len(nrow(parameter_grid)), 10, FALSE)
      parameter_grid <- kdry::mlh_subset(parameter_grid, sample_rows)
    }

    # required for bayesian optimization
    parameter_bounds <- list(
      minsplit = c(2L, 100L),
      cp = c(0.01, 0.1),
      maxdepth = c(2L, 30L)
    )
    optim_args <- list(
      n_iter = ncores,
      kappa = 3.5,
      acq = "ucb"
    )

## Hyperparameter Tuning

### Grid Search

    tuner <- mlexperiments::MLTuneParameters$new(
      learner = LearnerRpart$new(),
      strategy = "grid",
      ncores = ncores,
      seed = seed
    )

    tuner$parameter_grid <- parameter_grid
    tuner$learner_args <- learner_args
    tuner$split_type <- "stratified"

    tuner$set_data(
      x = train_x,
      y = train_y,
      cat_vars = cat_vars
    )

    tuner_results_grid <- tuner$execute(k = 3)
    #>
    #>  Regression: using 'mean squared error' as optimization metric.
    #>
    #>  Regression: using 'mean squared error' as optimization metric.
    #>
    #>  Regression: using 'mean squared error' as optimization metric.
    #>
    #>  Regression: using 'mean squared error' as optimization metric.
    #>
    #>  Regression: using 'mean squared error' as optimization metric.
    #>
    #>  Regression: using 'mean squared error' as optimization metric.
    #>
    #>  Regression: using 'mean squared error' as optimization metric.
    #>
    #>  Regression: using 'mean squared error' as optimization metric.
    #>
    #> Parameter settings [=====================================================================================>----------] 9/10 ( 90%)
    #>  Regression: using 'mean squared error' as optimization metric.
    #>
    #> Parameter settings [===============================================================================================] 10/10 (100%)
    #>  Regression: using 'mean squared error' as optimization metric.

    head(tuner_results_grid)
    #>    setting_id metric_optim_mean minsplit   cp maxdepth method
    #> 1:          1          26.14038        2 0.07       22  anova
    #> 2:          2          26.14038       32 0.02       27  anova
    #> 3:          3          26.14038       72 0.10        7  anova
    #> 4:          4          26.14038       32 0.09       27  anova
    #> 5:          5          26.14038       52 0.02       12  anova
    #> 6:          6          26.14038        2 0.04        7  anova

### Bayesian Optimization

    tuner <- mlexperiments::MLTuneParameters$new(
      learner = LearnerRpart$new(),
      strategy = "bayesian",
      ncores = ncores,
      seed = seed
    )

    tuner$parameter_grid <- parameter_grid
    tuner$parameter_bounds <- parameter_bounds

    tuner$learner_args <- learner_args
    tuner$optim_args <- optim_args

    tuner$split_type <- "stratified"

    tuner$set_data(
      x = train_x,
      y = train_y,
      cat_vars = cat_vars
    )

    tuner_results_bayesian <- tuner$execute(k = 3)
    #>
    #> Registering parallel backend using 4 cores.

    head(tuner_results_bayesian)
    #>    Epoch setting_id minsplit   cp maxdepth gpUtility acqOptimum inBounds Elapsed     Score metric_optim_mean errorMessage method
    #> 1:     0          1        2 0.07       22        NA      FALSE     TRUE   0.049 -26.14038          26.14038           NA  anova
    #> 2:     0          2       32 0.02       27        NA      FALSE     TRUE   0.049 -26.14038          26.14038           NA  anova
    #> 3:     0          3       72 0.10        7        NA      FALSE     TRUE   0.049 -26.14038          26.14038           NA  anova
    #> 4:     0          4       32 0.09       27        NA      FALSE     TRUE   0.049 -26.14038          26.14038           NA  anova
    #> 5:     0          5       52 0.02       12        NA      FALSE     TRUE   0.027 -26.14038          26.14038           NA  anova
    #> 6:     0          6        2 0.04        7        NA      FALSE     TRUE   0.027 -26.14038          26.14038           NA  anova

## k-Fold Cross Validation

    validator <- mlexperiments::MLCrossValidation$new(
      learner = LearnerRpart$new(),
      fold_list = fold_list,
      ncores = ncores,
      seed = seed
    )

    validator$learner_args <- tuner$results$best.setting[-1]

    validator$predict_args <- predict_args
    validator$performance_metric <- performance_metric
    validator$performance_metric_args <- performance_metric_args
    validator$return_models <- return_models

    validator$set_data(
      x = train_x,
      y = train_y,
      cat_vars = cat_vars
    )

    validator_results <- validator$execute()
    #>
    #> CV fold: Fold1
    #>
    #> CV fold: Fold2
    #>
    #> CV fold: Fold3

    head(validator_results)
    #>     fold performance minsplit   cp maxdepth method
    #> 1: Fold1    29.20022        2 0.07       22  anova
    #> 2: Fold2    17.76631        2 0.07       22  anova
    #> 3: Fold3    31.45460        2 0.07       22  anova

## Nested Cross Validation

### Inner Grid Search

    validator <- mlexperiments::MLNestedCV$new(
      learner = LearnerRpart$new(),
      strategy = "grid",
      fold_list = fold_list,
      k_tuning = 3L,
      ncores = ncores,
      seed = seed
    )

    validator$parameter_grid <- parameter_grid
    validator$learner_args <- learner_args
    validator$split_type <- "stratified"

    validator$predict_args <- predict_args
    validator$performance_metric <- performance_metric
    validator$performance_metric_args <- performance_metric_args
    validator$return_models <- return_models

    validator$set_data(
      x = train_x,
      y = train_y,
      cat_vars = cat_vars
    )

    validator_results <- validator$execute()
    #>
    #> CV fold: Fold1
    #>
    #>  Regression: using 'mean squared error' as optimization metric.
    #>
    #>  Regression: using 'mean squared error' as optimization metric.
    #>
    #>  Regression: using 'mean squared error' as optimization metric.
    #>
    #>  Regression: using 'mean squared error' as optimization metric.
    #>
    #>  Regression: using 'mean squared error' as optimization metric.
    #>
    #>  Regression: using 'mean squared error' as optimization metric.
    #>
    #>  Regression: using 'mean squared error' as optimization metric.
    #>
    #>  Regression: using 'mean squared error' as optimization metric.
    #>
    #> Parameter settings [=====================================================================================>----------] 9/10 ( 90%)
    #>  Regression: using 'mean squared error' as optimization metric.
    #>
    #> Parameter settings [===============================================================================================] 10/10 (100%)
    #>  Regression: using 'mean squared error' as optimization metric.
    #>
    #> CV fold: Fold2
    #> CV progress [====================================================================>-----------------------------------] 2/3 ( 67%)
    #>
    #>  Regression: using 'mean squared error' as optimization metric.
    #>
    #>  Regression: using 'mean squared error' as optimization metric.
    #>
    #>  Regression: using 'mean squared error' as optimization metric.
    #>
    #>  Regression: using 'mean squared error' as optimization metric.
    #>
    #>  Regression: using 'mean squared error' as optimization metric.
    #>
    #>  Regression: using 'mean squared error' as optimization metric.
    #>
    #>  Regression: using 'mean squared error' as optimization metric.
    #>
    #>  Regression: using 'mean squared error' as optimization metric.
    #>
    #>  Regression: using 'mean squared error' as optimization metric.
    #>
    #> Parameter settings [===============================================================================================] 10/10 (100%)
    #>  Regression: using 'mean squared error' as optimization metric.
    #>
    #> CV fold: Fold3
    #> CV progress [========================================================================================================] 3/3 (100%)
    #>
    #>  Regression: using 'mean squared error' as optimization metric.
    #>
    #>  Regression: using 'mean squared error' as optimization metric.
    #>
    #>  Regression: using 'mean squared error' as optimization metric.
    #>
    #>  Regression: using 'mean squared error' as optimization metric.
    #>
    #>  Regression: using 'mean squared error' as optimization metric.
    #>
    #>  Regression: using 'mean squared error' as optimization metric.
    #>
    #>  Regression: using 'mean squared error' as optimization metric.
    #>
    #>  Regression: using 'mean squared error' as optimization metric.
    #>
    #> Parameter settings [=====================================================================================>----------] 9/10 ( 90%)
    #>  Regression: using 'mean squared error' as optimization metric.
    #>
    #> Parameter settings [===============================================================================================] 10/10 (100%)
    #>  Regression: using 'mean squared error' as optimization metric.

    head(validator_results)
    #>     fold performance minsplit   cp maxdepth method
    #> 1: Fold1    29.20022        2 0.07       22  anova
    #> 2: Fold2    17.76631        2 0.07       22  anova
    #> 3: Fold3    31.45460        2 0.07       22  anova

### Inner Bayesian Optimization

    validator <- mlexperiments::MLNestedCV$new(
      learner = LearnerRpart$new(),
      strategy = "bayesian",
      fold_list = fold_list,
      k_tuning = 3L,
      ncores = ncores,
      seed = seed
    )

    validator$parameter_grid <- parameter_grid
    validator$learner_args <- learner_args
    validator$split_type <- "stratified"

    validator$parameter_bounds <- parameter_bounds
    validator$optim_args <- optim_args

    validator$predict_args <- predict_args
    validator$performance_metric <- performance_metric
    validator$performance_metric_args <- performance_metric_args
    validator$return_models <- TRUE

    validator$set_data(
      x = train_x,
      y = train_y,
      cat_vars = cat_vars
    )

    validator_results <- validator$execute()
    #>
    #> CV fold: Fold1
    #>
    #> Registering parallel backend using 4 cores.
    #>
    #> CV fold: Fold2
    #> CV progress [====================================================================>-----------------------------------] 2/3 ( 67%)
    #>
    #> Registering parallel backend using 4 cores.
    #>
    #> CV fold: Fold3
    #> CV progress [========================================================================================================] 3/3 (100%)
    #>
    #> Registering parallel backend using 4 cores.

    head(validator_results)
    #>     fold performance minsplit   cp maxdepth method
    #> 1: Fold1    29.20022        2 0.07       22  anova
    #> 2: Fold2    17.76631        2 0.07       22  anova
    #> 3: Fold3    31.45460        2 0.07       22  anova

## Comparison with Linear Regression

See https://github.com/kapsner/mlexperiments/blob/main/R/learner_lm.R for implementation details.

    validator_lm <- mlexperiments::MLCrossValidation$new(
      learner = LearnerLm$new(),
      fold_list = fold_list,
      ncores = ncores,
      seed = seed
    )

    validator_lm$predict_args <- list(type = "response")
    validator_lm$performance_metric <- performance_metric
    validator_lm$performance_metric_args <- performance_metric_args
    validator_lm$return_models <- TRUE

    validator_lm$set_data(
      x = train_x,
      y = train_y,
      cat_vars = cat_vars
    )

    validator_lm_results <- validator_lm$execute()
    #>
    #> CV fold: Fold1
    #> Parameter 'ncores' is ignored for learner 'LearnerLm'.
    #>
    #> CV fold: Fold2
    #> Parameter 'ncores' is ignored for learner 'LearnerLm'.
    #>
    #> CV fold: Fold3
    #> Parameter 'ncores' is ignored for learner 'LearnerLm'.

    head(validator_lm_results)
    #>     fold performance
    #> 1: Fold1    35.49058
    #> 2: Fold2    22.04977
    #> 3: Fold3    21.39721

### Test Fold Equality

    mlexperiments::validate_fold_equality(
      experiments = list(validator, validator_lm)
    )
    #>
    #> Testing for identical folds in 1 and 2.
    #>
    #> Testing for identical folds in 2 and 1.

### Predict Outcome in Holdout Test Dataset

    preds_rpart <- mlexperiments::predictions(
      object = validator,
      newdata = test_x,
      cat_vars = cat_vars
    )

    preds_lm <- mlexperiments::predictions(
      object = validator_lm,
      newdata = test_x,
      cat_vars = cat_vars
    )

### Evaluate Performance on Holdout Test Dataset

    perf_rpart <- mlexperiments::performance(
      object = validator,
      prediction_results = preds_rpart,
      y_ground_truth = test_y,
      type = "regression"
    )

    perf_lm <- mlexperiments::performance(
      object = validator_lm,
      prediction_results = preds_lm,
      y_ground_truth = test_y,
      type = "regression"
    )

    # combine results for plotting
    final_results <- rbind(
      cbind(algorithm = "rpart", perf_rpart),
      cbind(algorithm = "lm", perf_lm)
    )

    # p <- ggpubr::ggdotchart(
    #   data = final_results,
    #   x = "algorithm",
    #   y = "mse",
    #   color = "model",
    #   rotate = TRUE
    # )
    # p

Model Comparison