`EpistasisSpline`¶

EpistasisSpline fits a smoothing spline as the nonlinear scale between the additive genetic score and the observed phenotype. Where EpistasisPowerTransform assumes a specific parametric shape, the spline can follow an arbitrary smooth scale, including non-monotonic ones. It is a concrete subclass of EpistasisNonlinearRegression backed by scipy.interpolate.UnivariateSpline.

Observed phenotype against the additive score, with the fitted smoothing-spline scale following a non-monotonic shape

The example scale dips before rising again. A power transform could not capture that shape, but the spline tracks it. The trade-off is that the spline is not monotone by construction, so it can chase noise if under-smoothed.

When to use this model¶

Use EpistasisSpline when the measurement scale is smooth but its functional form is unknown or non-monotonic, and you would rather let the data choose the shape than commit to a parametric transform. If you know the scale is monotone, prefer EpistasisMonotonicGE or EpistasisPowerTransform, which cannot produce a spurious wiggle.

How it works¶

The same two-stage fit as EpistasisNonlinearRegression: an order-1 additive model produces a per-genotype additive score, then a univariate smoothing spline is fit mapping the additive score to the observed phenotypes. Duplicate x-values get deterministic jitter so the spline solver stays well-posed.

Constructor parameters¶

k (int, default 3): Spline degree. 3 is a cubic smoothing spline.
s (float | None, default None): Smoothing factor passed to UnivariateSpline. Smaller values follow the data more closely (and risk overfitting); larger values smooth more. None lets scipy choose from the data.
model_type (str, default "global"): Encoding for the additive design matrix: "global" (Hadamard) or "local".
seed (int | None, default 0): Seed for the deterministic jitter applied to duplicate x-values.

Workflow¶

from epistasis.models.nonlinear import EpistasisSpline

model = EpistasisSpline(k=3, model_type="global")
model.add_gpm(gpm)
model.fit()

y_pred = model.predict()
y_linear = model.transform()
r2 = model.score()

Key methods and attributes¶

Member	Description
`fit(X=None, y=None)`	Two-stage fit: additive model, then the smoothing spline.
`predict(X=None)`	Predicted phenotype on the observed scale.
`transform(X=None, y=None)`	Observed phenotypes projected back onto the additive scale.
`score(X=None, y=None)`	Pearson R^2 between observed and predicted.
`model.minimizer`	`SplineMinimizer`; wraps the fitted `UnivariateSpline`.

See the two-stage fitting guide, EpistasisPowerTransform, and EpistasisMonotonicGE.

EpistasisSpline¶