# Mining Invariance from Nonlinear Multi-Environment Data: Binary Classification

arXiv: https://arxiv.org/abs/2404.15245 · HTML: https://mlsanity.com/paper/2404.15245/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 21 references that are in the map.
- First posted on arXiv 23 Apr 2024.

## Builds on (most cited first, 10 of 10)

- [Causal inference using invariant prediction: identification and confidence intervals](https://mlsanity.com/paper/1501.01332/) (2015)
- [Invariant Causal Prediction for Nonlinear Models](https://mlsanity.com/paper/1706.08576/) (2017)
- [Anchor regression: heterogeneous data meets causality](https://mlsanity.com/paper/1801.06229/) (2018)
- [Invariant Causal Prediction for Sequential Data](https://mlsanity.com/paper/1706.08058/) (2017)
- [Stabilizing Variable Selection and Regression](https://mlsanity.com/paper/1911.01850/) (2019)
- [Estimating and Explaining Model Performance When Both Covariates and Labels Shift](https://mlsanity.com/paper/2209.08436/) (2022)
- [Sparse joint shift in multinomial classification](https://mlsanity.com/paper/2303.16971/) (2023)
- [Learning Invariant Representations under General Interventions on the Response](https://mlsanity.com/paper/2208.10027/) (2022)
- [Generalized Invariant Matching Property via LASSO](https://mlsanity.com/paper/2301.05975/) (2023)
- [Error Probability Bounds for Invariant Causal Prediction via Multiple Access Channels](https://mlsanity.com/paper/2308.10119/) (2023)

## Abstract (arXiv)

Making predictions in an unseen environment given data from multiple training environments is a challenging task. We approach this problem from an invariance perspective, focusing on binary classification to shed light on general nonlinear data generation mechanisms. We identify a unique form of invariance that exists solely in a binary setting that allows us to train models invariant over environments. We provide sufficient conditions for such invariance and show it is robust even when environmental conditions vary greatly. Our formulation admits a causal interpretation, allowing us to compare it with various frameworks. Finally, we propose a heuristic prediction method and conduct experiments using real and synthetic datasets.