ElasticNet via ADMM

The ElasticNet estimator solves the elastic-net problem using ADMM (Alternating Direction Method of Multipliers). It supports six distribution families: Gaussian, Binomial, Poisson, Gamma, Tweedie, and Multinomial.

Gaussian regression

Gaussian is the default and most common family.

import numpy as np
from pflm.pflm.utils import ElasticNet

rng = np.random.default_rng(0)
n, p = 200, 5
X = rng.standard_normal((n, p))
true_coef = np.array([1.5, -2.0, 0.0, 0.0, 3.0])
y = X @ true_coef + 0.5 * rng.standard_normal(n)

model = ElasticNet(alpha=0.1, l1_ratio=0.5)
model.fit(X, y)
print("Coefficients:", model.coef_)
print("Intercept:", model.intercept_)

# Predict on new data
X_new = rng.standard_normal((10, p))
y_pred = model.predict(X_new)
print("Predictions:", y_pred[:5])

Logistic regression (Binomial)

For binary classification, use the Binomial family. predict returns probabilities ∈ (0, 1).

from pflm.pflm.utils import ElasticNet, LinearModelFamily

rng = np.random.default_rng(42)
n, p = 300, 4
X = rng.standard_normal((n, p))
prob = 1 / (1 + np.exp(-(X @ np.array([1.0, -0.5, 0.0, 2.0]))))
y = rng.binomial(1, prob).astype(float)

model = ElasticNet(alpha=0.05, l1_ratio=0.8, family=LinearModelFamily.BINOMIAL)
model.fit(X, y)
probs = model.predict(X[:5])
print("Predicted probabilities:", probs)

Poisson regression

For count data use the Poisson family. predict returns the rate λ = exp(Xβ).

from pflm.pflm.utils import ElasticNet, LinearModelFamily

rng = np.random.default_rng(7)
n, p = 200, 3
X = rng.standard_normal((n, p))
lam = np.exp(X @ np.array([0.5, -0.3, 0.2]))
y = rng.poisson(lam).astype(float)

model = ElasticNet(alpha=0.01, l1_ratio=0.5, family=LinearModelFamily.POISSON)
model.fit(X, y)
print("Coefficients:", model.coef_)

Tuning the ADMM solver

The rho, abs_tol, rel_tol, max_iter and min_iter parameters control the ADMM convergence behaviour.

model = ElasticNet(
    alpha=0.1,
    l1_ratio=0.9,
    rho=2.0,           # larger rho → faster primal convergence
    max_iter=2000,
    abs_tol=1e-6,
    rel_tol=1e-7,
    min_iter=5,
)
model.fit(X, y)
print(f"Converged in {model.n_iter} iterations")