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arXiv · 2405.19540

Computing Low-Entropy Couplings for Large-Support Distributions

Samuel Sokota·Dylan Sam·Christian Schroeder de Witt·Spencer Compton·Jakob Foerster·J. Zico Kolter
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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 .

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Samuel Sokota, Dylan Sam, Christian Schroeder de Witt, Spencer Compton, Jakob Foerster, J. Zico Kolter. 2024-05-29. Computing Low-Entropy Couplings for Large-Support Distributions. https://arxiv.org/abs/2405.19540

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