Scikit-Learn GridSearchCV PLSRegression

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 PLSRegression, a regression technique suited for datasets with multicollinearity.

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.

PLSRegression (Partial Least Squares Regression) is used for predicting a set of dependent variables from a set of independent variables. It is particularly useful when the predictors are highly collinear or when the number of predictors exceeds the number of observations.

The key hyperparameters for PLSRegression include the number of components (n_components), which determines the dimensionality reduction, and scale, which indicates whether to scale the predictors before applying the regression.

from sklearn.datasets import make_regression
from sklearn.model_selection import train_test_split, GridSearchCV
from sklearn.cross_decomposition import PLSRegression

# Generate synthetic regression dataset
X, y = make_regression(n_samples=1000, n_features=10, n_informative=8, 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 = {
    'n_components': [2, 4, 6, 8, 10],
    'scale': [True, False]
}

# Perform grid search
grid_search = GridSearchCV(estimator=PLSRegression(),
                           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 R^2 score: {test_score:.3f}")

Running the example gives an output like:

Best score: -0.009
Best parameters: {'n_components': 6, 'scale': True}
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 parameter grid with different values for n_components and scale hyperparameters.
4. Perform grid search using GridSearchCV, specifying the PLSRegression model, parameter grid, 5-fold cross-validation, and negative mean squared error as the scoring metric.
5. Report the best cross-validation score and the best set of hyperparameters found by grid search.
6. Evaluate the best model on the hold-out test set and report the R^2 score.

By using GridSearchCV, we can efficiently explore different hyperparameter settings and find the configuration that maximizes the performance of the PLSRegression model. This automated approach simplifies the hyperparameter tuning process and ensures the best model setup for our regression task.