Subjective Distortion: Achievability and Outer Bounds for Distortion Functions with Memory

TL;DR

This paper introduces a formal framework for rate-distortion problems where distortion depends on past actions, providing bounds and convexification techniques, with applications in biological processing and recommendation systems.

Contribution

It formalizes the concept of subjective distortion with memory, deriving inner and outer bounds on the rate-distortion tradeoff and discussing convexification methods.

Findings

Derived achievable and outer bounds for distortion with memory

Applied convexification to simplify bounds calculation

Provided an example in biological information processing

Abstract

In some rate-distortion-type problems, the required fidelity of information is affected by past actions. As a result, the distortion function depends not only on the instantaneous distortion between a source symbol and its representation symbol, but also on past representations. In this paper, we give a formal definition of this problem and introduce both inner (achievable) and outer bounds on the rate-distortion tradeoff. We also discuss convexification of the problem, which makes it easier to find bounds. Problems of this type arise in biological information processing, as well as in recommendation engines; we provide an example applied to a simplified biological information processing problem.