Scikit-Learn GridSearchCV PoissonRegressor

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 PoissonRegressor, a popular algorithm for modeling count data.

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.

PoissonRegressor is used for modeling count data and assumes the target variable follows a Poisson distribution. It is suitable for datasets where the outcome variable is a count of events.

The key hyperparameters for PoissonRegressor include the regularization strength (alpha), which helps prevent overfitting; the fit_intercept parameter, which determines whether to calculate the intercept for the model; and the max_iter, which specifies the maximum number of iterations for the solver to converge.

from sklearn.datasets import make_regression
from sklearn.model_selection import train_test_split, GridSearchCV
from sklearn.linear_model import PoissonRegressor
import numpy as np

# Generate synthetic count data
rng = np.random.RandomState(42)
X = rng.randn(1000, 10)
y = rng.poisson(lam=np.exp(0.5 * X[:, 0] - 0.3 * X[:, 1]), size=1000)

# 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 = {
    'alpha': [0.1, 1, 10],
    'fit_intercept': [True, False],
    'max_iter': [100, 500, 1000]
}

# Perform grid search
grid_search = GridSearchCV(estimator=PoissonRegressor(),
                           param_grid=param_grid,
                           cv=5,
                           scoring='neg_mean_poisson_deviance')
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: -1.138
Best parameters: {'alpha': 0.1, 'fit_intercept': False, 'max_iter': 100}
Test set score: 0.285

The steps are as follows:

1. Generate a synthetic dataset using a Poisson distribution to simulate count data.
2. Split the dataset into train and test sets using train_test_split.
3. Define the parameter grid with different values for alpha, fit_intercept, and max_iter hyperparameters.
4. Perform grid search using GridSearchCV, specifying the PoissonRegressor model, parameter grid, 5-fold cross-validation, and negative mean Poisson deviance as the 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 effectively explore different hyperparameter settings and find the configuration that maximizes the model’s performance for count data using PoissonRegressor. This approach automates hyperparameter tuning, ensuring optimal performance with minimal manual effort.