Comparing randomized search and grid search for hyperparameter estimation

Compare randomized search and grid search for optimizing hyperparameters of a random forest. All parameters that influence the learning are searched simultaneously (except for the number of estimators, which poses a time / quality tradeoff).

The randomized search and the grid search explore exactly the same space of parameters. The result in parameter settings is quite similar, while the run time for randomized search is drastically lower.

The performance is slightly worse for the randomized search, though this is most likely a noise effect and would not carry over to a held-out test set.

Note that in practice, one would not search over this many different parameters simultaneously using grid search, but pick only the ones deemed most important.

Out:

RandomizedSearchCV took 3.80 seconds for 20 candidates parameter settings.
Model with rank: 1
Mean validation score: 0.928 (std: 0.021)
Parameters: {'bootstrap': False, 'criterion': 'entropy', 'max_depth': None, 'max_features': 9, 'min_samples_leaf': 2, 'min_samples_split': 2}

Model with rank: 2
Mean validation score: 0.925 (std: 0.015)
Parameters: {'bootstrap': False, 'criterion': 'gini', 'max_depth': None, 'max_features': 10, 'min_samples_leaf': 1, 'min_samples_split': 6}

Model with rank: 3
Mean validation score: 0.912 (std: 0.004)
Parameters: {'bootstrap': False, 'criterion': 'entropy', 'max_depth': None, 'max_features': 3, 'min_samples_leaf': 7, 'min_samples_split': 5}

GridSearchCV took 37.20 seconds for 216 candidate parameter settings.
Model with rank: 1
Mean validation score: 0.935 (std: 0.008)
Parameters: {'bootstrap': False, 'criterion': 'gini', 'max_depth': None, 'max_features': 3, 'min_samples_leaf': 1, 'min_samples_split': 3}

Model with rank: 2
Mean validation score: 0.932 (std: 0.012)
Parameters: {'bootstrap': False, 'criterion': 'gini', 'max_depth': None, 'max_features': 10, 'min_samples_leaf': 1, 'min_samples_split': 3}

Model with rank: 3
Mean validation score: 0.931 (std: 0.018)
Parameters: {'bootstrap': False, 'criterion': 'entropy', 'max_depth': None, 'max_features': 10, 'min_samples_leaf': 1, 'min_samples_split': 10}

print(__doc__)

import numpy as np

from time import time
from scipy.stats import randint as sp_randint

from sklearn.model_selection import GridSearchCV
from sklearn.model_selection import RandomizedSearchCV
from sklearn.datasets import load_digits
from sklearn.ensemble import RandomForestClassifier

# get some data
digits = load_digits()
X, y = digits.data, digits.target

# build a classifier
clf = RandomForestClassifier(n_estimators=20)


# Utility function to report best scores
def report(results, n_top=3):
    for i in range(1, n_top + 1):
        candidates = np.flatnonzero(results['rank_test_score'] == i)
        for candidate in candidates:
            print("Model with rank: {0}".format(i))
            print("Mean validation score: {0:.3f} (std: {1:.3f})".format(
                  results['mean_test_score'][candidate],
                  results['std_test_score'][candidate]))
            print("Parameters: {0}".format(results['params'][candidate]))
            print("")


# specify parameters and distributions to sample from
param_dist = {"max_depth": [3, None],
              "max_features": sp_randint(1, 11),
              "min_samples_split": sp_randint(2, 11),
              "min_samples_leaf": sp_randint(1, 11),
              "bootstrap": [True, False],
              "criterion": ["gini", "entropy"]}

# run randomized search
n_iter_search = 20
random_search = RandomizedSearchCV(clf, param_distributions=param_dist,
                                   n_iter=n_iter_search)

start = time()
random_search.fit(X, y)
print("RandomizedSearchCV took %.2f seconds for %d candidates"
      " parameter settings." % ((time() - start), n_iter_search))
report(random_search.cv_results_)

# use a full grid over all parameters
param_grid = {"max_depth": [3, None],
              "max_features": [1, 3, 10],
              "min_samples_split": [2, 3, 10],
              "min_samples_leaf": [1, 3, 10],
              "bootstrap": [True, False],
              "criterion": ["gini", "entropy"]}

# run grid search
grid_search = GridSearchCV(clf, param_grid=param_grid)
start = time()
grid_search.fit(X, y)

print("GridSearchCV took %.2f seconds for %d candidate parameter settings."
      % (time() - start, len(grid_search.cv_results_['params'])))
report(grid_search.cv_results_)

Total running time of the script: ( 0 minutes 41.142 seconds)

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