# Distributional Extrapolation for Interactions

arXiv: https://arxiv.org/abs/2608.19849 · HTML: https://mlsanity.com/paper/2608.19849/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 19 of its 41 references that are in the map.
- First posted on arXiv 20 Aug 2026.

## Builds on (most cited first, 19 of 19)

- [Invariant Risk Minimization](https://mlsanity.com/paper/1907.02893/) (2019)
- [Out-of-Distribution Generalization via Risk Extrapolation (REx)](https://mlsanity.com/paper/2003.00688/) (2020)
- [OpenML: networked science in machine learning](https://mlsanity.com/paper/1407.7722/) (2014)
- [Neural Additive Models: Interpretable Machine Learning with Neural Nets](https://mlsanity.com/paper/2004.13912/) (2020)
- [How Neural Networks Extrapolate: From Feedforward to Graph Neural Networks](https://mlsanity.com/paper/2009.11848/) (2020)
- [Generalization in Deep Learning](https://mlsanity.com/paper/1710.05468/) (2017)
- [Understanding the Failure Modes of Out-of-Distribution Generalization](https://mlsanity.com/paper/2010.15775/) (2020)
- [Anchor regression: heterogeneous data meets causality](https://mlsanity.com/paper/1801.06229/) (2018)
- [HPOBench: A Collection of Reproducible Multi-Fidelity Benchmark Problems for HPO](https://mlsanity.com/paper/2109.06716/) (2021)
- [Learning in High Dimension Always Amounts to Extrapolation](https://mlsanity.com/paper/2110.09485/) (2021)
- [Engression: Extrapolation through the Lens of Distributional Regression](https://mlsanity.com/paper/2307.00835/) (2023)
- [On the Generalization Mystery in Deep Learning](https://mlsanity.com/paper/2203.10036/) (2022)
- [When does compositional structure yield compositional generalization? A kernel theory](https://mlsanity.com/paper/2405.16391/) (2024)
- [Learning to Extrapolate: A Transductive Approach](https://mlsanity.com/paper/2304.14329/) (2023)
- [Distributional Principal Autoencoders](https://mlsanity.com/paper/2404.13649/) (2024)
- [Tackling Combinatorial Distribution Shift: A Matrix Completion Perspective](https://mlsanity.com/paper/2307.06457/) (2023)
- [Extrapolation-Aware Nonparametric Statistical Inference](https://mlsanity.com/paper/2402.09758/) (2024)
- [A General Theory for Compositional Generalization](https://mlsanity.com/paper/2405.11743/) (2024)
- [Deep learning with missing data](https://mlsanity.com/paper/2504.15388/) (2025)

## Abstract (arXiv)

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.