A Short Information-Theoretic Analysis of Linear Auto-Regressive Learning

TL;DR

This paper provides an information-theoretic proof of the consistency of Gaussian maximum likelihood estimators in linear auto-regressive models, offering nearly optimal non-asymptotic rates without stability assumptions.

Contribution

It introduces a novel information-theoretic proof technique that achieves near-optimal rates for parameter recovery in linear auto-regressive models.

Findings

Proves consistency of Gaussian MLE in linear AR models

Derives nearly optimal non-asymptotic recovery rates

Operates without stability assumptions in finite hypothesis classes

Abstract

In this note, we give a short information-theoretic proof of the consistency of the Gaussian maximum likelihood estimator in linear auto-regressive models. Our proof yields nearly optimal non-asymptotic rates for parameter recovery and works without any invocation of stability in the case of finite hypothesis classes.