Compressing Multisets With Large Alphabets

Current methods which compress multisets at an optimal rate have computational complexity that scales linearly with alphabet size, making them too slow to be practical in many real-world settings. We show how convert a compression algorithm for sequences into one multisets, exchange additional term is quasi-linear sequence length. This allows us of exchangeable symbols rate, decoupled from the size. The key insight avoid encoding multiset directly, and instead proxy sequence, using technique called bits-back coding. demonstrate method experimentally on tasks are intractable previous optimal-rate methods: images JavaScript Object Notation (JSON) files. Code our experiments available https://github.com/facebookresearch/multiset-compression.