Log-Likelihood Loss for Semantic Compression

TL;DR

This paper introduces a new framework for lossy source coding using a log-likelihood based distortion measure, focusing on semantic representations that enable probabilistic source reconstruction.

Contribution

It formulates the rate-distortion problem under log-likelihood distortion and explores its fundamental properties and connections to existing compression paradigms.

Findings

Characterizes the rate-distortion function with log-likelihood distortion.

Establishes connections to lossy compression under log-loss and classical rate-distortion.

Provides insights into rate-distortion with perfect perception.

Abstract

We study lossy source coding under a distortion measure defined by the negative log-likelihood induced by a prescribed conditional distribution $P_{X|U}$. This \emph{log-likelihood distortion} models compression settings in which the reconstruction is a semantic representation from which the source can be probabilistically generated, rather than a pointwise approximation. We formulate the corresponding rate-distortion problem and characterize fundamental properties of the resulting rate-distortion function, including its connections to lossy compression under log-loss, classical rate-distortion problems with arbitrary distortion measures, and rate-distortion with perfect perception.