Joint universal lossy coding and identification of i.i.d. vector sources

TL;DR

This paper extends the concept of joint universal source coding and modeling to lossy compression of continuous i.i.d. vector sources, providing theoretical guarantees and explicit examples for such schemes.

Contribution

It introduces a joint scheme for universal lossy coding and parameter estimation for continuous i.i.d. sources under certain conditions, with convergence rate estimates.

Findings

Achieves joint universal lossy coding and modeling for bounded distortion measures.

Provides nonasymptotic convergence rate estimates.

Includes explicit examples of parametric sources with such schemes.

Abstract

The problem of joint universal source coding and modeling, addressed by Rissanen in the context of lossless codes, is generalized to fixed-rate lossy coding of continuous-alphabet memoryless sources. We show that, for bounded distortion measures, any compactly parametrized family of i.i.d. real vector sources with absolutely continuous marginals (satisfying appropriate smoothness and Vapnik--Chervonenkis learnability conditions) admits a joint scheme for universal lossy block coding and parameter estimation, and give nonasymptotic estimates of convergence rates for distortion redundancies and variational distances between the active source and the estimated source. We also present explicit examples of parametric sources admitting such joint universal compression and modeling schemes.