Scikit-Learn RandomizedSearchCV TheilSenRegressor

Hyperparameter tuning is essential for optimizing machine learning models. In this example, we’ll demonstrate how to use scikit-learn’s RandomizedSearchCV for hyperparameter tuning of a TheilSenRegressor model, known for its robustness against outliers in regression tasks.

Random search is a method for evaluating different combinations of model hyperparameters. Unlike grid search, it samples a fixed number of hyperparameter combinations from a specified distribution, making it more efficient when searching over a large hyperparameter space.

TheilSenRegressor is a robust linear regression model that estimates the relationship between the dependent variable and independent variables while being resilient to outliers. The model is trained by repeatedly fitting subsets of the data and finding the median of these fits.

Key hyperparameters for TheilSenRegressor include the maximum subpopulation size (max_subpopulation), which determines the size of the random subsets used in each iteration; the maximum number of iterations (max_iter), which controls the number of iterations for the fitting process; and the tolerance (tol), which is the stopping criterion for the iterations.

from sklearn.datasets import make_regression
from sklearn.model_selection import train_test_split, RandomizedSearchCV
from sklearn.linear_model import TheilSenRegressor
from scipy.stats import randint, uniform

# Generate synthetic regression dataset
X, y = make_regression(n_samples=1000, n_features=10, noise=0.1, random_state=42)

# Split into train and test sets
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=42)

# Define the model
model = TheilSenRegressor(random_state=42)

# Define hyperparameter distribution
param_dist = {
    'max_subpopulation': randint(1, 100),
    'max_iter': randint(30, 1000),
    'tol': uniform(1e-4, 1e-1)
}

# Perform random search
random_search = RandomizedSearchCV(estimator=model,
                                   param_distributions=param_dist,
                                   n_iter=100,
                                   cv=5,
                                   scoring='neg_mean_squared_error',
                                   random_state=42)
random_search.fit(X_train, y_train)

# Report best score and parameters
print(f"Best score: {random_search.best_score_:.3f}")
print(f"Best parameters: {random_search.best_params_}")

# Evaluate on test set
best_model = random_search.best_estimator_
test_score = best_model.score(X_test, y_test)
print(f"Test set R^2 score: {test_score:.3f}")

Running the example gives an output like:

Best score: -0.012
Best parameters: {'max_iter': 706, 'max_subpopulation': 97, 'tol': 0.012086536733368281}
Test set R^2 score: 1.000

The steps are as follows:

1. Generate a synthetic regression dataset using scikit-learn’s make_regression function.
2. Split the dataset into train and test sets using train_test_split.
3. Define the model TheilSenRegressor.
4. Specify hyperparameter distributions for max_subpopulation, max_iter, and tol.
5. Perform random search using RandomizedSearchCV, specifying the TheilSenRegressor model, hyperparameter distribution, 100 iterations, 5-fold cross-validation, and negative mean squared error scoring metric.
6. Report the best cross-validation score and best set of hyperparameters found by random search.
7. Evaluate the best model on the hold-out test set and report the R^2 score.

By using RandomizedSearchCV, we can efficiently explore different hyperparameter settings and find the combination that maximizes the model’s performance. This automated approach saves time and effort compared to manual hyperparameter tuning and helps ensure we select the best configuration for our TheilSenRegressor model.