Skip to content
conftrace_
2025 L4DC L4DC 2025

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

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.

Authors

Ingvar Ziemann

Topics

Machine Learning > Optimization & Theory > Learning Theory Machine Learning > Optimization & Theory > Information Theory Machine Learning > Learning Types > Time Series Analysis

Keywords

information theory parameter recovery autoregressive model maximum likelihood estimator non-asymptotic rate
Download PDF

More from L4DC 2025

All L4DC 2025 papers →
State space models, emergence, and ergodicity: How many parameters are needed for stable predictions?
Multi-agent Stochastic Bandits Robust to Adversarial Corruptions
Exploiting Approximate Symmetry for Efficient Multi-Agent Reinforcement Learning
DiffuSolve: Diffusion-based Solver for Non-convex Trajectory Optimization
DKMGP: A Gaussian Process Approach to Multi-Task and Multi-Step Vehicle Dynamics Modeling in Autonomous Racing
Asymptotics of Linear Regression with Linearly Dependent Data