eikgp-regressor 0.1.1

Numerically stable EIKG polynomial regressors

EIKGP Regressor

EIKGPolynomialRegressor is a compact two-stage regression model inspired by the elementary image of a Kolmogorov-Gabor polynomial:

1. Linear latent stage: z = b0 + b1*x1 + ... + bm*xm
2. Polynomial output stage: y_hat = a0 + a1*z + a2*z^2 + ... + ad*z^d

This implementation is built for numerical stability and sklearn-style workflows.

Important warning

The model is a compressed elementary image of the Kolmogorov-Gabor polynomial and is not equivalent to direct estimation of the full multivariate polynomial basis.

Installation

From PyPI (after release):

pip install eikgp-regressor

From source (editable):

pip install -e .

With optional dependencies:

pip install -e ".[dev]"

Basic usage

import numpy as np
from eikg import EIKGPolynomialRegressor

rng = np.random.default_rng(42)
X = rng.normal(size=(200, 3))
z = 1.0 + 1.8 * X[:, 0] - 0.9 * X[:, 1]
y = z + 0.15 * z**2 + rng.normal(0, 0.1, size=200)

model = EIKGPolynomialRegressor(
    degree=3,
    regularization="ridge",
    alpha_ridge=1e-5,
    scale=True,
    normalize_latent=True,
)
model.fit(X, y)
pred = model.predict(X)
print(model.score(X, y))

Pipeline example

from sklearn.pipeline import Pipeline
from sklearn.preprocessing import StandardScaler
from eikg import EIKGPolynomialRegressor

pipe = Pipeline(
    [
        ("scaler", StandardScaler()),
        ("model", EIKGPolynomialRegressor(scale=False, degree=2)),
    ]
)
pipe.fit(X, y)

GridSearchCV example

from sklearn.model_selection import GridSearchCV
from eikg import EIKGPolynomialRegressor

search = GridSearchCV(
    EIKGPolynomialRegressor(),
    param_grid={
        "degree": [1, 2, 3, 4],
        "regularization": ["none", "ridge"],
        "alpha_ridge": [1e-8, 1e-5, 1e-3],
    },
    scoring="neg_mean_squared_error",
    cv=5,
)
search.fit(X, y)
print(search.best_params_)

Automatic degree selection

from eikg import EIKGPolynomialRegressorCV

cv_model = EIKGPolynomialRegressorCV(
    max_degree=6,
    cv=5,
    scoring="neg_mean_squared_error",
    regularization="ridge",
    alpha_ridge=1e-5,
)
cv_model.fit(X, y)
print(cv_model.selected_degree_, cv_model.best_score_)

Main limitations

• Model expressiveness is bounded by one latent linear projection.
• Very high degree can still be unstable without meaningful scaling/normalization.
• Quality of fit depends on whether target structure is well-approximated by polynomial-in-latent form.

Development quality checks

ruff check .
mypy eikg
pytest

You can install git hooks for automatic local checks:

pre-commit install
pre-commit run --all-files

Build and publish

Build distribution artifacts:

python -m pip install -e ".[dev]"
python -m build
python -m twine check dist/*

Upload to TestPyPI:

python -m twine upload --repository testpypi dist/*

Upload to PyPI:

python -m twine upload dist/*