Entropy Coding of Unordered Data Structures

Julius Kunze, Daniel Severo, Giulio Zani, Jan-Willem van de Meent, James Townsend

Keywords: graph compression, entropy coding, neural compression, bits-back coding, lossless compression, generative models, information theory, probabilistic models, graph neural networks, multiset compression, asymmetric numeral systems, compression, entropy, shuffle coding

TL;DR: We present shuffle coding, a general method for optimal compression of unordered objects, achieving state-of-the-art compression rates on a range of graph datasets including molecular data.

Abstract: We present shuffle coding, a general method for optimal compression of sequences of unordered objects using bits-back coding. Data structures that can be compressed using shuffle coding include multisets, graphs, hypergraphs, and others. We demonstrate that the method achieves state-of-the-art compression rates on a range of graph datasets including molecular data, and release an implementation that can easily be adapted to different data types and statistical models.

Submission Number: 16