Computing Low-Entropy Couplings for Large-Support Distributions

TL;DR

This paper introduces ARIMEC, a new algorithm for computing minimum-entropy couplings in large-support distributions, improving robustness and applicability in fields like steganography and causality.

Contribution

The paper unifies existing IMEC methods into a generalized framework and develops ARIMEC, a versatile, robust algorithm for arbitrary discrete distributions.

Findings

ARIMEC handles large-support distributions efficiently.

The method is robust to hyperparameter choices.

Application demonstrated in high-throughput steganography.

Abstract

Minimum-entropy coupling (MEC) -- the process of finding a joint distribution with minimum entropy for given marginals -- has applications in areas such as causality and steganography. However, existing algorithms are either computationally intractable for large-support distributions or limited to specific distribution types and sensitive to hyperparameter choices. This work addresses these limitations by unifying a prior family of iterative MEC (IMEC) approaches into a generalized partition-based formalism. From this framework, we derive a novel IMEC algorithm called ARIMEC, capable of handling arbitrary discrete distributions, and introduce a method to make IMEC robust to suboptimal hyperparameter settings. These innovations facilitate the application of IMEC to high-throughput steganography with language models, among other settings. Our codebase is available at https://github.com/ssokota/mec .