Scikit-Learn RandomizedSearchCV PoissonRegressor

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 Poisson regression model, commonly used for count data modeling.

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.

Poisson regression is used for modeling count data where the response variable follows a Poisson distribution. It is particularly useful for predicting the number of events occurring within a fixed period.

Key hyperparameters for Poisson regression include the regularization strength (alpha), which controls model complexity and helps prevent overfitting; the fit_intercept, which indicates whether to calculate the intercept for the model; and 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, RandomizedSearchCV
from sklearn.linear_model import PoissonRegressor
from scipy.stats import uniform

# Generate synthetic count data (non-negative integers)
X, y = make_regression(n_samples=1000, n_features=10, noise=0.1, random_state=42)
y = abs(y.astype(int))  # Ensure target is count data

# 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 hyperparameter distribution
param_dist = {
    'alpha': uniform(loc=0, scale=1),
    'fit_intercept': [True, False],
    'max_iter': [100, 200, 300]
}

# Perform random search
random_search = RandomizedSearchCV(estimator=PoissonRegressor(),
                                   param_distributions=param_dist,
                                   n_iter=100,
                                   cv=5,
                                   scoring='neg_mean_poisson_deviance',
                                   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_
accuracy = best_model.score(X_test, y_test)
print(f"Test set accuracy: {accuracy:.3f}")

Running the example gives an output like:

Best score: -62.677
Best parameters: {'alpha': 0.9717120953891037, 'fit_intercept': True, 'max_iter': 100}
Test set accuracy: -0.019

The steps are as follows:

1. Generate a synthetic count dataset using scikit-learn’s make_regression function and convert targets to non-negative integers.
2. Split the dataset into train and test sets using train_test_split.
3. Define a hyperparameter distribution with different values for alpha, fit_intercept, and max_iter hyperparameters.
4. Perform random search using RandomizedSearchCV, specifying the PoissonRegressor model, hyperparameter distribution, 100 iterations, 5-fold cross-validation, and the negative mean Poisson deviance scoring metric.
5. Report the best cross-validation score and best set of hyperparameters found by random search.
6. Evaluate the best model on the hold-out test set and report the accuracy.

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 Poisson regression model.