Improving Lossless Compression Rates via Monte Carlo Bits-Back Coding

TL;DR

This paper introduces Monte Carlo bits-back coding algorithms that leverage tighter variational bounds and extended space representations to asymptotically eliminate the KL divergence gap, improving lossless compression rates especially in challenging data scenarios.

Contribution

It develops novel bits-back coding algorithms based on tighter variational bounds and Monte Carlo estimators, reducing the bitrate gap caused by KL divergence.

Findings

Achieves better compression rates than standard bits-back coding.

Effectively reduces additional initial bits through latent space couplings.

Demonstrates improved performance in out-of-distribution and sequential data compression.

Abstract

Latent variable models have been successfully applied in lossless compression with the bits-back coding algorithm. However, bits-back suffers from an increase in the bitrate equal to the KL divergence between the approximate posterior and the true posterior. In this paper, we show how to remove this gap asymptotically by deriving bits-back coding algorithms from tighter variational bounds. The key idea is to exploit extended space representations of Monte Carlo estimators of the marginal likelihood. Naively applied, our schemes would require more initial bits than the standard bits-back coder, but we show how to drastically reduce this additional cost with couplings in the latent space. When parallel architectures can be exploited, our coders can achieve better rates than bits-back with little additional cost. We demonstrate improved lossless compression rates in a variety of settings, especially in out-of-distribution or sequential data compression.