Analysis of Mismatched Estimation Errors Using Gradients of Partition Functions

TL;DR

This paper analyzes mismatched estimation errors in signal denoising using partition functions, deriving explicit formulas and illustrating phase transitions through examples to deepen understanding of estimation behavior.

Contribution

It introduces a novel statistical-mechanical approach to derive single-letter mismatched MSE expressions and explores phase transitions in estimation performance.

Findings

Derived explicit mismatched MSE formulas

Identified phase transition phenomena in estimation errors

Provided examples illustrating the impact of probability measures

Abstract

We consider the problem of signal estimation (denoising) from a statistical-mechanical perspective, in continuation to a recent work on the analysis of mean-square error (MSE) estimation using a direct relationship between optimum estimation and certain partition functions. The paper consists of essentially two parts. In the first part, using the aforementioned relationship, we derive single-letter expressions of the mismatched MSE of a codeword (from a randomly selected code), corrupted by a Gaussian vector channel. In the second part, we provide several examples to demonstrate phase transitions in the behavior of the MSE. These examples enable us to understand more deeply and to gather intuition regarding the roles of the real and the mismatched probability measures in creating these phase transitions.