erbf 0.1.0

Ellipsoidal RBF network regressor with gradient-optimized anisotropic widths

erbf

Ellipsoidal RBF network regressor with gradient-optimised anisotropic widths.

Installation

pip install erbf

Quick start

from erbf import ERBFRegressor
from sklearn.datasets import make_friedman1
from sklearn.model_selection import train_test_split

X, y = make_friedman1(n_samples=1000, random_state=42)
X_train, X_test, y_train, y_test = train_test_split(X, y, random_state=42)

model = ERBFRegressor(n_rbf=40, random_state=42)
model.fit(X_train, y_train)
print(f"R2: {model.score(X_test, y_test):.3f}")

Key features

• Anisotropic widths --- per-feature per-RBF width parameters capture axis-aligned structure
• Gradient optimisation --- L-BFGS-B in log-space with analytical gradients; O(n K d) per iteration
• Modular initialisation --- Lipschitz-guided centre placement, local-Ridge width initialisation
• scikit-learn compatible --- fit/predict/score, clone(), get_params()/set_params()

How it works

ERBFRegressor places K radial basis functions in the feature space, each with a per-dimension width vector that controls sensitivity along each axis. Centres are initialised by sampling from high-gradient regions (Lipschitz-guided), widths are initialised via local Ridge regression coefficients, then both widths and output weights are jointly refined. Width optimisation operates in log-space via L-BFGS-B with analytical gradients, preventing width collapse and ensuring a smooth loss landscape.

Parameters

Parameter	Default	Description
n_rbf	40	Number of RBF centres ('auto' for adaptive)
center_init	'lipschitz'	Centre placement: 'lipschitz', 'kmeans', 'random'
width_init	'local_ridge'	Width initialisation: 'local_ridge', 'local_variance', 'uniform'
width_mode	'full'	Parameterisation: 'full' (K*d), 'shared' (d), 'isotropic' (K)
width_optim	'gradient'	Optimisation: 'gradient' (L-BFGS-B) or None
alpha	1.0	Ridge regularisation strength
standardize	True	Standardise features before fitting

Citation

@article{gerber2026revisiting,
  title={Revisiting Chebyshev Polynomial and Anisotropic RBF Models for Tabular Regression},
  author={Gerber, Luciano and Lloyd, Chris},
  year={2026}
}

Licence

MIT