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arXiv · 2608.19849

Distributional Extrapolation for Interactions

Marin Šola·Xinwei Shen·Peter Bühlmann
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Abstract

Predicting combinatorial effects from limited-range observations is a fundamental challenge in many scientific domains, including drug discovery and hyperparameter optimization. We study combinatorial extrapolation, where training data consists of axis-aligned samples with only one active covariate, while test-time inputs involve multiple simultaneously active covariates. We introduce DExtrI, a method for extrapolating interaction effects beyond the support of the training data. We provide theoretical guarantees characterizing when such extrapolation is possible. Empirical results on synthetic and real-world datasets demonstrate that DExtrI successfully generalizes to unseen combinations of covariates. Our approach enables applications such as predicting previously untested drug combinations and improving the efficiency of hyperparameter optimization.

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Marin Šola, Xinwei Shen, Peter Bühlmann. 2026-08-20. Distributional Extrapolation for Interactions. https://arxiv.org/abs/2608.19849

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