# Environment-Adaptive Covariate Selection: Learning When to Use Spurious Correlations for Out-of-Distribution Prediction

arXiv: https://arxiv.org/abs/2601.02322 · HTML: https://mlsanity.com/paper/2601.02322/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 31 references that are in the map.
- First posted on arXiv 5 Jan 2026.

## Builds on (most cited first, 20 of 20)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Invariant Risk Minimization](https://mlsanity.com/paper/1907.02893/) (2019)
- [Deep Sets](https://mlsanity.com/paper/1703.06114/) (2017)
- [Causal inference using invariant prediction: identification and confidence intervals](https://mlsanity.com/paper/1501.01332/) (2015)
- [Retiring Adult: New Datasets for Fair Machine Learning](https://mlsanity.com/paper/2108.04884/) (2021)
- [Towards Causal Representation Learning](https://mlsanity.com/paper/2102.11107/) (2021)
- [CAM: Causal additive models, high-dimensional order search and penalized regression](https://mlsanity.com/paper/1310.1533/) (2013)
- [Invariant Causal Prediction for Nonlinear Models](https://mlsanity.com/paper/1706.08576/) (2017)
- [Invariance, Causality and Robustness](https://mlsanity.com/paper/1812.08233/) (2018)
- [Anchor regression: heterogeneous data meets causality](https://mlsanity.com/paper/1801.06229/) (2018)
- [Benchmarking Distribution Shift in Tabular Data with TableShift](https://mlsanity.com/paper/2312.07577/) (2023)
- [Probabilistic Best Subset Selection via Gradient-Based Optimization](https://mlsanity.com/paper/2006.06448/) (2020)
- [Environment Invariant Linear Least Squares](https://mlsanity.com/paper/2303.03092/) (2023)
- [Do causal predictors generalize better to new domains?](https://mlsanity.com/paper/2402.09891/) (2024)
- [Out-of-distribution generalization under random, dense distributional shifts](https://mlsanity.com/paper/2404.18370/) (2024)
- [Are Domain Generalization Benchmarks with Accuracy on the Line Misspecified?](https://mlsanity.com/paper/2504.00186/) (2025)
- [Reassessing the Validity of Spurious Correlations Benchmarks](https://mlsanity.com/paper/2409.04188/) (2024)
- [OOD-Chameleon: Is Algorithm Selection for OOD Generalization Learnable?](https://mlsanity.com/paper/2410.02735/) (2024)
- [Bayesian Invariance Modeling of Multi-Environment Data](https://mlsanity.com/paper/2506.22675/) (2025)

## Built on by (most cited first, 1 of 1)

- [Chaos Is a LADDER: Domain Generalization Beyond Invariance via Reweighting](https://mlsanity.com/paper/2607.26458/) (2026)

## Abstract (arXiv)

A common approach to out-of-distribution prediction restricts models to causal or invariant covariates to avoid spurious associations that may change across environments. Despite its theoretical appeal, this strategy can underperform empirical risk minimization when only a subset of the causal parents of the outcome is observed. In such settings, non-causal covariates can serve as proxies for unobserved causal parents and improve prediction when the proxy relationship is stable, but they can hurt when shifts disrupt that relationship. Thus, the optimal covariate set can depend on the specific shift encountered. Because different shifts leave signatures in the unlabeled covariate distribution, we propose an environment-adaptive covariate selection algorithm that maps environment-level summaries to environment-specific covariate sets. These summaries may be hand-crafted or learned from multi-environment data, and prior causal knowledge can be incorporated as constraints. Across simulations and applied datasets, the proposed method improves over static causal, invariant, and other non-adaptive rules under diverse shifts.