Scikit-Learn GridSearchCV TheilSenRegressor

Hyperparameter tuning is a crucial step in optimizing machine learning models for best performance. In this example, we’ll demonstrate how to use scikit-learn’s GridSearchCV to perform hyperparameter tuning for TheilSenRegressor, a robust linear regression model.

Grid search is a method for evaluating different combinations of model hyperparameters to find the best performing configuration. It exhaustively searches through a specified parameter grid, trains and evaluates the model for each combination using cross-validation, and selects the hyperparameters that yield the best performance metric.

TheilSenRegressor is a robust linear regression model that is less sensitive to outliers compared to standard linear regression. It estimates the regression coefficients by considering all possible combinations of subsets of the input data, making it a robust choice for datasets with outliers.

The key hyperparameters for TheilSenRegressor include the maximum number of subpopulations to consider (max_subpopulation), the number of samples to be drawn for calculating the estimate (n_subsamples), whether to calculate the intercept for the model (fit_intercept), and the maximum number of iterations for the solver (max_iter).

from sklearn.datasets import make_regression
from sklearn.model_selection import train_test_split, GridSearchCV
from sklearn.linear_model import TheilSenRegressor

# Generate synthetic regression dataset
X, y = make_regression(n_samples=100, 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 parameter grid
param_grid = {
    'max_subpopulation': [1e2, 1e3],
    'n_subsamples': [10, 50],
    'fit_intercept': [True, False],
    'max_iter': [10, 50]
}

# Perform grid search
grid_search = GridSearchCV(estimator=TheilSenRegressor(random_state=42),
                           param_grid=param_grid,
                           cv=5,
                           scoring='neg_mean_squared_error')
grid_search.fit(X_train, y_train)

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

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

Running the example gives an output like:

Best score: -0.013
Best parameters: {'fit_intercept': True, 'max_iter': 10, 'max_subpopulation': 100.0, 'n_subsamples': 50}
Test set score: 1.000

The steps are as follows:

1. Generate a synthetic regression dataset using make_regression.
2. Split the dataset into train and test sets using train_test_split.
3. Define the parameter grid with different values for max_subpopulation, n_subsamples, fit_intercept, and max_iter.
4. Perform grid search using GridSearchCV, specifying the TheilSenRegressor model, parameter grid, 5-fold cross-validation, and negative mean squared error scoring metric.
5. Report the best cross-validation score and best set of hyperparameters found by grid search.
6. Evaluate the best model on the hold-out test set and report the score.

By using GridSearchCV, we can easily 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.