New Family of Generalization Bounds Using Samplewise Evaluated CMI
Paper in proceeding, 2022

We present a new family of information-theoretic generalization bounds, in which the training loss and the population loss are compared through a jointly convex function. This function is upper-bounded in terms of the disintegrated, samplewise, evaluated conditional mutual information (CMI), an information measure that depends on the losses incurred by the selected hypothesis, rather than on the hypothesis itself, as is common in probably approximately correct (PAC)-Bayesian results. We demonstrate the generality of this framework by recovering and extending previously known information-theoretic bounds. Furthermore, using the evaluated CMI, we derive a samplewise, average version of Seeger's PAC-Bayesian bound, where the convex function is the binary KL divergence. In some scenarios, this novel bound results in a tighter characterization of the population loss of deep neural networks than previous bounds. Finally, we derive high-probability versions of some of these average bounds. We demonstrate the unifying nature of the evaluated CMI bounds by using them to recover average and high-probability generalization bounds for multiclass classification with finite Natarajan dimension.

PAC-Bayes

Machine learning

Information theory

Generalization bounds

Deep learning

Author

Fredrik Hellström

Chalmers, Electrical Engineering, Communication, Antennas and Optical Networks

Giuseppe Durisi

Chalmers, Electrical Engineering, Communication, Antennas and Optical Networks

Advances in Neural Information Processing Systems

10495258 (ISSN)

Vol. 35
9781713871088 (ISBN)

Conference on Neural Information Processing Systems (NeurIPS)
New Orleans, USA,

Areas of Advance

Information and Communication Technology

Subject Categories

Computational Mathematics

Probability Theory and Statistics

Mathematical Analysis

More information

Latest update

1/3/2024 9