From Invariant Representations to Invariant Data: Provable Robustness to Spurious Correlations via Noisy Counterfactual Matching

TL;DR

This paper introduces Noisy Counterfactual Matching (NCM), a data-centric approach that enhances model robustness to spurious correlations by leveraging noisy counterfactual data pairs, backed by theoretical guarantees and empirical validation.

Contribution

The paper proposes NCM, a novel method that uses noisy counterfactual pairs to improve robustness against spurious correlations, providing theoretical bounds and empirical evidence.

Findings

NCM improves robustness with noisy counterfactual pairs.

Theoretical bounds relate test error to in-domain error and counterfactual quality.

Empirical results validate NCM's effectiveness on real datasets.

Abstract

Models that learn spurious correlations from training data often fail when deployed in new environments. While many methods aim to learn invariant representations to address this, they often underperform standard empirical risk minimization (ERM). We propose a data-centric alternative that shifts the focus from learning invariant representations to leveraging invariant data pairs -- pairs of samples that should have the same prediction. We prove that certain counterfactuals naturally satisfy this invariance property. Based on this, we introduce Noisy Counterfactual Matching (NCM), a simple constraint-based method that improves robustness by leveraging even a small number of \emph{noisy} counterfactual pairs -- improving upon prior works that do not explicitly consider noise. For linear causal models, we prove that NCM's test-domain error is bounded by its in-domain error plus a term dependent on the counterfactuals' quality and diversity. Experiments on synthetic data validate our theory, and we demonstrate NCM's effectiveness on real-world datasets.