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

arXiv: https://arxiv.org/abs/2409.06437 · HTML: https://mlsanity.com/paper/2409.06437/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 4 of its 7 references that are in the map.
- First posted on arXiv 10 Sep 2024.

## Builds on (most cited first, 4 of 4)

- [Information-theoretic analysis of generalization capability of learning algorithms](https://mlsanity.com/paper/1705.07809/) (2017)
- [Learning Without Mixing: Towards A Sharp Analysis of Linear System Identification](https://mlsanity.com/paper/1802.08334/) (2018)
- [Sharp Rates in Dependent Learning Theory: Avoiding Sample Size Deflation for the Square Loss](https://mlsanity.com/paper/2402.05928/) (2024)
- [Information-Theoretic Foundations for Machine Learning](https://mlsanity.com/paper/2407.12288/) (2024)

## Abstract (arXiv)

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.