tidymodels-tree1

statlearning

trees

tidymodels

string

mtcars

Published

November 8, 2023

library(tidymodels)

Aufgabe

Berechnen Sie folgende prädiktiven Modelle und vergleichen Sie die Modellgüte:

Entscheidungsbaum
Bagging (Bootstrap-Bäume)

Modellformel: am ~ . (Datensatz mtcars)

Berichten Sie die Modellgüte (ROC-AUC).

Hinweise:

Tunen Sie alle Parameter (die der Engine anbietet).
Verwenden Sie Defaults, wo nicht anders angegeben.
Führen Sie eine \(v=2\)-fache Kreuzvalidierung durch (weil die Stichprobe so klein ist).
Beachten Sie die üblichen Hinweise.

Lösung

Setup

library(tidymodels)
data(mtcars)
library(tictoc)  # Zeitmessung
library(baguette)

Für Klassifikation verlangt Tidymodels eine nominale AV, keine numerische:

mtcars <-
  mtcars %>% 
  mutate(am = factor(am))

Daten teilen

d_split <- initial_split(mtcars)
d_train <- training(d_split)
d_test <- testing(d_split)

Modell(e)

mod_tree <-
  decision_tree(mode = "classification",
                cost_complexity = tune(),
                tree_depth = tune(),
                min_n = tune())

mod_bag <-
  bag_tree(mode = "classification",
           cost_complexity = tune(),
           tree_depth = tune(),
           min_n = tune())

Rezept(e)

rec_plain <- 
  recipe(am ~ ., data = d_train)

Resampling

rsmpl <- vfold_cv(d_train, v = 2)

Workflows

wf_tree <-
  workflow() %>%  
  add_recipe(rec_plain) %>% 
  add_model(mod_tree)

wf_bag <-
  workflow() %>%  
  add_recipe(rec_plain) %>% 
  add_model(mod_bag)

Tuning/Fitting

Tuninggrid:

tune_grid <- grid_regular(extract_parameter_set_dials(mod_tree), levels = 5)
tune_grid

# A tibble: 125 × 3
   cost_complexity tree_depth min_n
             <dbl>      <int> <int>
 1    0.0000000001          1     2
 2    0.0000000178          1     2
 3    0.00000316            1     2
 4    0.000562              1     2
 5    0.1                   1     2
 6    0.0000000001          4     2
 7    0.0000000178          4     2
 8    0.00000316            4     2
 9    0.000562              4     2
10    0.1                   4     2
# ℹ 115 more rows

Da beide Modelle die gleichen Tuningparameter aufweisen, brauchen wir nur ein Grid zu erstellen.

tic()
fit_tree <-
  tune_grid(object = wf_tree,
            grid = tune_grid,
            metrics = metric_set(roc_auc),
            resamples = rsmpl)
toc()

18.258 sec elapsed

fit_tree

# Tuning results
# 2-fold cross-validation 
# A tibble: 2 × 4
  splits          id    .metrics           .notes           
  <list>          <chr> <list>             <list>           
1 <split [12/12]> Fold1 <tibble [125 × 7]> <tibble [75 × 3]>
2 <split [12/12]> Fold2 <tibble [125 × 7]> <tibble [75 × 3]>

There were issues with some computations:

  - Warning(s) x50: 21 samples were requested but there were 12 rows in the data. 12 ...
  - Warning(s) x50: 30 samples were requested but there were 12 rows in the data. 12 ...
  - Warning(s) x50: 40 samples were requested but there were 12 rows in the data. 12 ...

Run `show_notes(.Last.tune.result)` for more information.

tic()
fit_bag <-
  tune_grid(object = wf_bag,
            grid = tune_grid,
            metrics = metric_set(roc_auc),
            resamples = rsmpl)
toc()

97.331 sec elapsed

Bester Kandidat

show_best(fit_tree)

# A tibble: 5 × 9
  cost_complexity tree_depth min_n .metric .estimator  mean     n std_err
            <dbl>      <int> <int> <chr>   <chr>      <dbl> <int>   <dbl>
1    0.0000000001          1     2 roc_auc binary     0.845     2  0.0119
2    0.0000000178          1     2 roc_auc binary     0.845     2  0.0119
3    0.00000316            1     2 roc_auc binary     0.845     2  0.0119
4    0.000562              1     2 roc_auc binary     0.845     2  0.0119
5    0.1                   1     2 roc_auc binary     0.845     2  0.0119
# ℹ 1 more variable: .config <chr>

show_best(fit_bag)

# A tibble: 5 × 9
  cost_complexity tree_depth min_n .metric .estimator  mean     n std_err
            <dbl>      <int> <int> <chr>   <chr>      <dbl> <int>   <dbl>
1    0.00000316            8     2 roc_auc binary     0.967     2 0.00423
2    0.00000316           11     2 roc_auc binary     0.967     2 0.00423
3    0.0000000178         15     2 roc_auc binary     0.967     2 0.00423
4    0.0000000001          4    11 roc_auc binary     0.967     2 0.00423
5    0.0000000178         11     2 roc_auc binary     0.965     2 0.0206 
# ℹ 1 more variable: .config <chr>

Bagging erzielte eine klar bessere Modellgüte (in den Validierungssamples) als das Entscheidungsbaum-Modell.

Finalisieren

wf_best_finalized <-
  wf_bag %>% 
  finalize_workflow(select_best(fit_bag))

Last Fit

final_fit <- 
  last_fit(object = wf_best_finalized, d_split)

collect_metrics(final_fit)

# A tibble: 3 × 4
  .metric     .estimator .estimate .config             
  <chr>       <chr>          <dbl> <chr>               
1 accuracy    binary       1       Preprocessor1_Model1
2 roc_auc     binary       1       Preprocessor1_Model1
3 brier_class binary       0.00103 Preprocessor1_Model1

Wie man sieht, ist die Modellgüte im Test-Sample schlechter als in den Train- bzw. Validierungssamples; ein typischer Befund.

Categories:

statlearning
trees
tidymodels
string