Exact results on high-dimensional linear regression via statistical physics

TL;DR

This paper applies statistical physics methods to derive exact results for high-dimensional linear regression, providing rigorous benchmarks for approximation techniques in modern high-dimensional data analysis.

Contribution

It introduces a novel application of statistical physics to obtain precise analytical results in high-dimensional linear regression, advancing theoretical understanding.

Findings

Derived exact formulas for high-dimensional linear regression

Provided rigorous benchmarks for approximation methods

Enhanced theoretical understanding of high-dimensional inference

Abstract

It is clear that conventional statistical inference protocols need to be revised to deal correctly with the high-dimensional data that are now common. Most recent studies aimed at achieving this revision rely on powerful approximation techniques, that call for rigorous results against which they can be tested. In this context, the simplest case of high-dimensional linear regression has acquired significant new relevance and attention. In this paper we use the statistical physics perspective on inference to derive a number of new exact results for linear regression in the high-dimensional regime.