Mining Invariance from Nonlinear Multi-Environment Data: Binary Classification

TL;DR

This paper introduces a novel invariance-based approach for binary classification across multiple environments, providing theoretical insights and a heuristic method that enhances robustness in unseen environments.

Contribution

It identifies a unique invariance specific to binary data, offers sufficient conditions for its robustness, and proposes a heuristic prediction method validated on real and synthetic datasets.

Findings

Invariant models are robust to environmental variations.

The proposed heuristic improves prediction accuracy.

The framework admits a causal interpretation.

Abstract

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.