Invariance Principle Meets Information Bottleneck for Out-of-Distribution Generalization

The invariance principle from causality is at the heart of notable approaches as invariant risk minimization (IRM) that seek to address-of-distribution (OOD) generalization failures. Despite the promising, invariance principle-based approaches fail in common classification, where invariant (causal) features capture all the information about the. Are these failures due to the methods failing to capture the invariance? is the invariance principle itself insufficient? To answer these questions, revisit the fundamental assumptions in linear regression tasks, where-based approaches were shown to provably generalize OOD. In contrast the linear regression tasks, we show that for linear classification tasks we much stronger restrictions on the distribution shifts, or otherwise OOD is impossible. Furthermore, even with appropriate restrictions distribution shifts in place, we show that the invariance principle alone is. We prove that a form of the information bottleneck constraint with invariance helps address key failures when invariant features all the information about the label and also retains the existing when they do not. We propose an approach that incorporates both of principles and demonstrate its effectiveness in several experiments.