Enhancing Distributional Stability among Sub-populations

TL;DR

This paper introduces a new concept called distributional stability to improve machine learning model robustness under distributional shifts, proposing a novel algorithm and providing theoretical and empirical validation.

Contribution

It proposes the distributional stability notion, a learnability assumption, a generalization error bound, and a stable risk minimization algorithm for better OOD generalization.

Findings

The SRM algorithm improves model stability under distribution shifts.

Theoretical bounds support the effectiveness of the proposed approach.

Experimental results validate the approach's practical benefits.

Abstract

Enhancing the stability of machine learning algorithms under distributional shifts is at the heart of the Out-of-Distribution (OOD) Generalization problem. Derived from causal learning, recent works of invariant learning pursue strict invariance with multiple training environments. Although intuitively reasonable, strong assumptions on the availability and quality of environments are made to learn the strict invariance property. In this work, we come up with the ``distributional stability" notion to mitigate such limitations. It quantifies the stability of prediction mechanisms among sub-populations down to a prescribed scale. Based on this, we propose the learnability assumption and derive the generalization error bound under distribution shifts. Inspired by theoretical analyses, we propose our novel stable risk minimization (SRM) algorithm to enhance the model's stability w.r.t. shifts in prediction mechanisms ($Y|X$-shifts). Experimental results are consistent with our intuition and validate the effectiveness of our algorithm. The code can be found at https://github.com/LJSthu/SRM.