Implementation:Scikit learn Scikit learn GeneralizedLinearRegressor

Knowledge Sources	Scikit_learn Scikit-learn Docs
Domains	Machine Learning, Generalized Linear Models
Last Updated	2026-02-08 15:00 GMT

Overview

Concrete tool for regression via penalized Generalized Linear Models with exponential dispersion family distributions provided by scikit-learn.

Description

_GeneralizedLinearRegressor is the base class for GLM regressors in scikit-learn, fitting the mean of the target y as y_pred = h(X * w) with an inverse link function h. It minimizes an objective combining the unit deviance with L2 regularization. The module provides three public estimators: PoissonRegressor (log link, Poisson distribution), GammaRegressor (log link, Gamma distribution), and TweedieRegressor (configurable power parameter). These support both L-BFGS and Newton-Cholesky solvers.

Usage

Use PoissonRegressor for count data modeling (e.g., event frequencies), GammaRegressor for positive continuous targets with constant coefficient of variation (e.g., insurance claims), and TweedieRegressor when you need to model distributions in the Tweedie family with a specific power parameter. These are preferred over ordinary least squares when the target distribution is non-Gaussian.

Code Reference

Source Location

• Repository: scikit-learn
• File: sklearn/linear_model/_glm/glm.py

Signature

class _GeneralizedLinearRegressor(RegressorMixin, BaseEstimator):
    """Regression via a penalized Generalized Linear Model (GLM)."""

class PoissonRegressor(_GeneralizedLinearRegressor):
    """Generalized Linear Model with a Poisson distribution."""

class GammaRegressor(_GeneralizedLinearRegressor):
    """Generalized Linear Model with a Gamma distribution."""

class TweedieRegressor(_GeneralizedLinearRegressor):
    """Generalized Linear Model with a Tweedie distribution."""

Import

from sklearn.linear_model import PoissonRegressor, GammaRegressor, TweedieRegressor

I/O Contract

Inputs

Name	Type	Required	Description
alpha	float	No	Regularization strength multiplying the L2 penalty (default=1.0)
fit_intercept	bool	No	Whether to add a bias/intercept to the linear predictor (default=True)
solver	str	No	Optimization algorithm: 'lbfgs' or 'newton-cholesky' (default='lbfgs')
max_iter	int	No	Maximum number of iterations for the solver (default=100)
tol	float	No	Stopping criterion tolerance (default=1e-4)
warm_start	bool	No	Reuse previous solution as initialization (default=False)
verbose	int	No	Verbosity level for the solver (default=0)
power	float	No	Tweedie power parameter (TweedieRegressor only, default=0.0)
link	str	No	Link function: 'auto', 'identity', or 'log' (TweedieRegressor only)

Outputs

Name	Type	Description
coef_	ndarray of shape (n_features,)	Estimated coefficients for the features
intercept_	float	Intercept (bias) term in the model
n_iter_	int	Actual number of iterations used in the solver

Usage Examples

Basic Usage

from sklearn.linear_model import PoissonRegressor
import numpy as np

X = np.array([[1, 2], [2, 3], [3, 4], [4, 5]])
y = np.array([1, 3, 7, 12])

model = PoissonRegressor(alpha=0.5)
model.fit(X, y)
print("Coefficients:", model.coef_)
print("Predictions:", model.predict(X))

Related Pages

• Principle:Scikit_learn_Scikit_learn_Generalized_Linear_Models