On Leave-One-Out Conditional Mutual Information For Generalization

TL;DR

This paper introduces a new leave-one-out conditional mutual information measure to derive practical, interpretable generalization bounds for supervised learning, validated on deep learning image classification tasks.

Contribution

It proposes a novel loo-CMI measure that is easy to compute and connects to existing concepts like cross-validation and stability, improving generalization bounds.

Findings

Bounds are non-vacuous on large-scale image classification.

Loo-CMI bounds are computationally feasible and interpretable.

Empirical validation shows accurate prediction of generalization gap.

Abstract

We derive information theoretic generalization bounds for supervised learning algorithms based on a new measure of leave-one-out conditional mutual information (loo-CMI). Contrary to other CMI bounds, which are black-box bounds that do not exploit the structure of the problem and may be hard to evaluate in practice, our loo-CMI bounds can be computed easily and can be interpreted in connection to other notions such as classical leave-one-out cross-validation, stability of the optimization algorithm, and the geometry of the loss-landscape. It applies both to the output of training algorithms as well as their predictions. We empirically validate the quality of the bound by evaluating its predicted generalization gap in scenarios for deep learning. In particular, our bounds are non-vacuous on large-scale image-classification tasks.