Towards Empirical Sandwich Bounds on the Rate-Distortion Function
arXiv:2111.12166
Abstract
Rate-distortion (R-D) function, a key quantity in information theory, characterizes the fundamental limit of how much a data source can be compressed subject to a fidelity criterion, by any compression algorithm. As researchers push for ever-improving compression performance, establishing the R-D function of a given data source is not only of scientific interest, but also sheds light on the possible room for improving compression algorithms. Previous work on this problem relied on distributional assumptions on the data source (Gibson, 2017) or only applied to discrete data (Blahut, 1972; Arimoto, 1972). By contrast, this paper makes the first attempt at an algorithm for sandwiching the R-D function of a general (not necessarily discrete) source requiring only i.i.d. data samples. We estimate R-D sandwich bounds for a variety of artificial and real-world data sources, in settings far beyond the feasibility of any known method, and shed light on the optimality of neural data compression (Ballé et al., 2021; Yang et al., 2022). Our R-D upper bound on natural images indicates theoretical room for improving state-of-the-art image compression methods by at least one dB in PSNR at various bitrates. Our data and code can be found at https://github.com/mandt-lab/empirical-RD-sandwich.
ICLR 2022 camera-ready version
References in corpus (7)
- The Concrete Distribution: A Continuous Relaxation of Discrete Random Variables
- On Variational Bounds of Mutual Information
- Improving Inference for Neural Image Compression
- Practical Lossless Compression with Latent Variables using Bits Back Coding
- The Intrinsic Dimension of Images and Its Impact on Learning
- Evaluating Lossy Compression Rates of Deep Generative Models
- Finding the Mode of a Kernel Density Estimate