`EpistasisMonotonicGE`¶

EpistasisMonotonicGE fits the nonlinear scale as a sum of K tanh sigmoids with non-negative coefficients, which makes the scale monotone by construction. It follows Tareen et al. 2022 (MAVE-NN, Genome Biology 23:98) and is the modern, identifiable alternative to EpistasisPowerTransform: the monotonicity constraint removes the sign ambiguity that hits unconstrained global-epistasis fits. It is a concrete subclass of EpistasisNonlinearRegression.

Observed phenotype against the additive score, with the fitted monotone tanh-sum scale

The fitted curve is guaranteed non-decreasing, so a higher additive score never maps to a lower predicted phenotype. With enough sigmoids (K) it can still capture sharp saturation, but it can never produce the spurious dips that an unconstrained or spline fit might.

When to use this model¶

Use EpistasisMonotonicGE when you believe the measurement scale is monotone (more additive signal never reduces the measured phenotype) and you want an identifiable, flexible fit. It is the recommended default for global-epistasis modeling when the power transform's specific shape is too rigid but a spline is too unconstrained.

How it works¶

The same two-stage fit as EpistasisNonlinearRegression: an order-1 additive model produces a per-genotype additive score, then a sum of K tanh sigmoids, f(x) = sum_k a_k * tanh(b_k * x + c_k) with b_k, c_k >= 0, is fit mapping the additive score to the observed phenotypes. The non-negativity constraints are what guarantee monotonicity and identifiability.

Constructor parameters¶

K (int, default 5): Number of tanh sigmoids in the sum. More sigmoids can represent sharper saturation at the cost of more parameters.
monotonic (bool, default True): Enforce the non-negativity constraints that make the scale monotone. Set False to relax them (rarely needed).
model_type (str, default "global"): Encoding for the additive design matrix: "global" (Hadamard) or "local".
seed (int | None, default 0): Seed for the optimizer's parameter initialization.

Workflow¶

from epistasis.models.nonlinear import EpistasisMonotonicGE

model = EpistasisMonotonicGE(K=5, monotonic=True, 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 monotone tanh-sum scale.
`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`	`MonotonicGEMinimizer`; holds the fitted sigmoid parameters.

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

EpistasisMonotonicGE¶