`ridge` — n4m.estimators.regression.regularized.ridge¶

Namespace: n4m.estimators.regression.regularized · Fully-qualified: n4m.estimators.regression.regularized.ridge · Catalog id: models.regularized.ridge

API surface¶

C ABI (ABI 2): n4m_estimators_ridge_fit. Use the linked public header for the exact signature, configuration, and result handles.

Python (verified public re-export): from n4m.estimators.regression.regularized import ridge

Signature: ridge(X, y, *, alpha: float = 1.0, center_x: bool | None = None, scale_x: bool | None = None, center_y: bool | None = None)

R (source-verified): ridge_fit(X, Y, n_components = 1L, ridge_lambda = 1.0).

library(n4m)
result <- ridge_fit(X, Y)

MATLAB / Octave: no current source-verified entry point was found for this catalog method.

Parameters¶

Name	Type	Default
`X`	`—`	`required`
`y`	`—`	`required`
`alpha`	`float`	`1.0`
`center_x`	`bool \| None`	`None`
`scale_x`	`bool \| None`	`None`
`center_y`	`bool \| None`	`None`

Explanations¶

Bibliographic source¶

Hoerl, A. E. & Kennard, R. W. (1970). Ridge Regression: Biased Estimation for Nonorthogonal Problems. Technometrics 12(1), 55–67. https://doi.org/10.1080/00401706.1970.10488634.

Mathematical principle¶

Estimate \(\hat{\beta}_\lambda=(X^\top X+\lambda I)^{-1}X^\top y\). The positive L2 penalty makes the normal equations invertible under collinearity and shrinks unstable coefficients toward zero without selecting features.

Appropriate uses¶

A linear calibration baseline for strongly collinear spectra or as the head of a strict-linear AOM route.

Limits and validation¶

The penalty changes with feature scale, so scaling belongs inside the fitting/CV protocol. Ridge retains all variables and its selected \(\lambda\) requires outer validation for an unbiased performance estimate.

Implementation¶

n4m.estimators.regression.regularized.ridge and RidgeRegressor; C ABI n4m_estimators_ridge_fit.

Sources and provenance¶

https://github.com/GBeurier/nirs4all-methods/blob/main/cpp/src/core/ridge.cpp; https://github.com/GBeurier/nirs4all-methods/blob/main/bindings/python/src/n4m/estimators/regression/regularized.py

Catalog note¶

Direct closed-form Ridge regression head with primal/dual handling in the native core. This is the reusable linear head used by the moment and AOM Ridge screens.

Timing benchmark: benchmarks/cross_binding/bench_direct_moment_heads_timing.py

See also: methods index.

ridge — n4m.estimators.regression.regularized.ridge¶