PoissonRegression

Guide & worked example · Source

PoissonRegression(optimizer=None, maxiter=5000, tol=0.0001, device=None)

Poisson Regression for count data with MLE estimation.

Estimates the relationship between count outcomes and covariates using the log link function. Assumes the conditional mean equals the conditional variance: E[y|X] = Var[y|X] = exp(X’β).

Examples: >>> model = PoissonRegression(maxiter=1000, tol=1e-6) >>> X = torch.randn(500, 4) >>> true_beta = torch.tensor([1.0, -0.5, 0.8, 0.3]) >>> y = torch.poisson(torch.exp(X @ true_beta)) >>> model.fit(X, y) >>> model.summary()

Attributes

Name	Description
device
history
maxiter
optimizer_class
params
tol

Methods

Name	Description
fit	Fit the model using maximum likelihood estimation.
predict	Predict expected counts E[y|X] = exp(X’β).
summary	Print a formatted summary of model estimation results.
to	Move model parameters and fitted data to device.

fit

PoissonRegression.fit(
    X,
    y,
    init_params=None,
    verbose=False,
    fe=None,
    fe_design=None,
    hdfe_index=None,
    offset=None,
    batch_size=None,
    stderr=True,
)

Fit the model using maximum likelihood estimation.

Optimizes the model parameters to minimize the negative log-likelihood using the specified PyTorch optimizer. After convergence, computes standard errors via the Fisher information matrix.

Args: X: Design matrix of shape (n_samples, n_features). Assumes X includes an intercept column if desired. y: Target vector of shape (n_samples,). init_params: Initial parameter values. For FE-aware GLMs, may be a packed parameter vector or a dict with coef and fe_coef. verbose: If True, prints convergence information. fe: Optional list of 1D fixed-effect ID vectors. fe_design: Optional list of sparse fixed-effect incidence matrices. hdfe_index: Optional index of the FE block to use for fast inference. offset: Optional offset vector added to the linear predictor. batch_size: Optional mini-batch size for first-order optimizers. stderr: Whether to compute standard errors.

Returns: Self (fitted estimator) with populated params dictionary.

Examples: >>> model = LogisticRegression() >>> model.fit(X_train, y_train, verbose=True) >>> print(model.params[“coef”])

predict

PoissonRegression.predict(X, fe=None, fe_design=None, offset=None)

Predict expected counts E[y|X] = exp(X’β).

Args: X: Design matrix of shape (n_samples, n_features). fe: Optional FE inputs for FE-aware models. fe_design: Optional sparse FE design inputs for FE-aware models. offset: Optional offset vector for FE-aware models.

Returns: Predicted expected counts of shape (n_samples,).

summary

PoissonRegression.summary(alpha=0.05)

Print a formatted summary of model estimation results.

Displays a comprehensive table including parameter estimates, standard errors, t-statistics, p-values, and confidence intervals (if standard errors are available).

Args: alpha: Significance level for confidence intervals (default: 0.05 for 95% confidence intervals).

Examples: >>> model.fit(X, y) >>> model.summary(alpha=0.01) # 99% confidence intervals

to

PoissonRegression.to(device)

Move model parameters and fitted data to device.