Improving Lossless Compression Rates via Monte Carlo Bits-Back Coding
This work addresses a bottleneck in lossless compression for data compression applications, offering incremental improvements over existing bits-back methods.
The paper tackles the problem of the increased bitrate in bits-back coding due to KL divergence by deriving algorithms from tighter variational bounds, achieving asymptotically better compression rates, especially for out-of-distribution or sequential data.
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.