On a Relation Between the Rate-Distortion Function and Optimal Transport

Eric Lei, Hamed Hassani, Shirin Saeedi Bidokhti
7/1/2023
cs.ITcs.LG

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Abstract

We discuss a relationship between rate-distortion and optimal transport (OT) theory, even though they seem to be unrelated at first glance. In particular, we show that a function defined via an extremal entropic OT distance is equivalent to the rate-distortion function. We numerically verify this result as well as previous results that connect the Monge and Kantorovich problems to optimal scalar quantization. Thus, we unify solving scalar quantization and rate-distortion functions in an alternative fashion by using their respective optimal transport solvers.

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Cite this paper

@article{lei2023relation,
  title  = {On a Relation Between the Rate-Distortion Function and Optimal Transport},
  author = {Eric Lei and Hamed Hassani and Shirin Saeedi Bidokhti},
  year   = {2023},
  eprint = {2307.00246},
  archivePrefix = {arXiv},
  url    = {http://arxiv.org/abs/2307.00246v1}
}

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