f-divergences and their applications in lossy compression and bounding generalization error
Abstract
In this paper, we provide three applications for -divergences: (i) we introduce Sanov's upper bound on the tail probability of the sum of independent random variables based on super-modular -divergence and show that our generalized Sanov's bound strictly improves over ordinary one, (ii) we consider the lossy compression problem which studies the set of achievable rates for a given distortion and code length. We extend the rate-distortion function using mutual -information and provide new and strictly better bounds on achievable rates in the finite blocklength regime using super-modular -divergences, and (iii) we provide a connection between the generalization error of algorithms with bounded input/output mutual -information and a generalized rate-distortion problem. This connection allows us to bound the generalization error of learning algorithms using lower bounds on the -rate-distortion function. Our bound is based on a new lower bound on the rate-distortion function that (for some examples) strictly improves over previously best-known bounds.
Cite
@article{arxiv.2206.11042,
title = {f-divergences and their applications in lossy compression and bounding generalization error},
author = {Saeed Masiha and Amin Gohari and Mohammad Hossein Yassaee},
journal= {arXiv preprint arXiv:2206.11042},
year = {2023}
}