Neural Estimation of the Rate-Distortion Function With Applications to Operational Source Coding

Abstract:  A fundamental question in designing lossy data compression schemes is how well one can do in comparison with the rate-distortion function, which describes the known theoretical limits of lossy compression. Motivated by the empirical success of deep neural network (DNN) compressors on large, real-world data, we investigate methods to estimate the rate-distortion function on such data, which would allow comparison of DNN compressors with optimality. While one could use the empirical distribution of the data and apply the Blahut-Arimoto algorithm, this approach presents several computational challenges and inaccuracies when the datasets are large and high-dimensional, such as the case of modern image datasets. Instead, we re-formulate the rate-distortion objective, and solve the resulting functional optimization problem using neural networks. We apply the resulting rate-distortion estimator, called NERD, on popular image datasets, and provide evidence that NERD can accurately estimate the rate-distortion function. Using our estimate, we show that the rate-distortion achievable by DNN compressors are within several bits of the rate-distortion function for real-world datasets. Additionally, NERD provides access to the rate-distortion achieving channel, as well as samples from its output marginal. Therefore, using recent results in reverse channel coding, we describe how NERD can be used to construct an operational one-shot lossy compression scheme with guarantees on the achievable rate and distortion. Experimental results demonstrate competitive performance with DNN compressors. Finally, we discuss several future research directions pertaining to techniques to make neural compressors optimal and scalable.

Bio: Shirin Saeedi Bidokhti is an assistant professor in the Department of Electrical and Systems Engineering at the University of Pennsylvania (UPenn). She received her M.Sc. and Ph.D. degrees in Computer and Communication Sciences from the Swiss Federal Institute of Technology (EPFL). Prior to joining UPenn, she was a postdoctoral scholar at Stanford University and the Technical University of Munich. She has also held short-term visiting positions at ETH Zurich, University of California at Los Angeles, and the Pennsylvania State University. Her research interests broadly include the design and analysis of network strategies that are scalable, practical, and efficient for use in Internet of Things (IoT) applications, information transfer on networks, as well as data compression techniques for big data. She is a recipient of the 2022 IT society Goldsmith lecturer award, 2021 NSF-CAREER award, 2019 NSF-CRII Research Initiative award and the prospective researcher and advanced postdoctoral fellowships from the Swiss National Science Foundation.