BaggedPolynomialRegressor

Bagged random-subspace polynomial ridge regression

from _api_doc_utils import *

1 Where it fits

Group: Regression

BaggedPolynomialRegressor is a prediction-only ensemble. Each base learner samples rows and a feature subspace, expands the selected features into monomials of total degree one through \(d\), standardizes those polynomial columns, fits ridge regression, and contributes to the averaged prediction.

For \(k\) selected features, each base learner uses

\[ \binom{k+d}{d}-1 \]

non-intercept polynomial terms. The estimator checks this count and the dense design size before allocation.

2 Python API

Constructor: cm.BaggedPolynomialRegressor

Use BaggedPolynomialRegressor(n_estimators, degree, max_features, max_samples, bootstrap, penalty, seed), then fit(x, y), predict(x), and summary(). It does not report coefficient standard errors. With bootstrap sampling, summary() reports out-of-bag MSE and coverage.

print(inspect.signature(cm.BaggedPolynomialRegressor))

display(HTML(html_table(["Public method"], public_methods(cm.BaggedPolynomialRegressor))))

3 Minimal example

rng = np.random.default_rng(18)
x = rng.normal(size=(320, 6))
y = 0.5 + 0.8 * x[:, 0] * x[:, 1] - 0.4 * x[:, 2] ** 2
y += rng.normal(scale=0.2, size=x.shape[0])

model = cm.BaggedPolynomialRegressor(
    n_estimators=40,
    degree=2,
    max_features=4,
    max_samples=240,
    penalty=0.5,
    seed=18,
)
model.fit(x, y)
print(model.predict(x[:3]))
print(model.summary()["oob_mse"])

4 summary() contract

summary = model.summary()
display(HTML(html_table(["summary() key", "shape"], summary_shape_rows(summary))))

max_features and max_samples are resolved fitted values rather than possible None constructor values. n_terms is the checked polynomial width per base learner. feature_indices records each random subspace. oob_mse is None when no observation receives an out-of-bag prediction.

5 Resource policy

Polynomial expansion is dense. The implementation rejects more than 100,000 polynomial terms per learner or more than 50 million cells in one polynomial design. Reduce degree, max_features, or max_samples when a guard triggers.