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Estimating the Rate-Distortion Function by Wasserstein Gradient Descent
Yibo Yang · Stephan Eckstein · Marcel Nutz · Stephan Mandt
Event URL: https://openreview.net/forum?id=5pt5Btjr8W »
In the theory of lossy compression, the rate-distortion function $R(D)$ of a given data source characterizes the fundamental limit of compression performance by any algorithm. We propose a method to estimate $R(D)$ in the continuous setting based on Wasserstein gradient descent. While the classic Blahut--Arimoto algorithm only optimizes probability weights over the support points of its initialization, our method leverages optimal transport theory and learns the support of the optimal reproduction distribution by moving particles. This makes it more suitable for high dimensional continuous problems. Our method complements state-of-the-art neural network-based methods in rate-distortion estimation, achieving comparable or improved results with less tuning and computation effort. In addition, we can derive its convergence and finite-sample properties analytically. Our study also applies to maximum likelihood deconvolution and regularized Kantorovich estimation, as those tasks boil down to mathematically equivalent minimization problems.

Author Information

Yibo Yang (University of California, Irivine)
Stephan Eckstein (ETHZ - ETH Zurich)
Marcel Nutz (Columbia University)
Stephan Mandt (University of California, Irivine)

Stephan Mandt is an Assistant Professor of Computer Science at the University of California, Irvine. From 2016 until 2018, he was a Senior Researcher and head of the statistical machine learning group at Disney Research, first in Pittsburgh and later in Los Angeles. He held previous postdoctoral positions at Columbia University and at Princeton University. Stephan holds a PhD in Theoretical Physics from the University of Cologne. He is a Fellow of the German National Merit Foundation, a Kavli Fellow of the U.S. National Academy of Sciences, and was a visiting researcher at Google Brain. Stephan serves regularly as an Area Chair for NeurIPS, ICML, AAAI, and ICLR, and is a member of the Editorial Board of JMLR. His research is currently supported by NSF, DARPA, IBM, and Qualcomm.

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