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

Ingvar Ziemann
Proceedings of the 7th Annual Learning for Dynamics \& Control Conference, PMLR 283:26-30, 2025.

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v283-ziemann25b, title = {A Short Information-Theoretic Analysis of Linear Auto-Regressive Learning}, author = {Ziemann, Ingvar}, booktitle = {Proceedings of the 7th Annual Learning for Dynamics \& Control Conference}, pages = {26--30}, year = {2025}, editor = {Ozay, Necmiye and Balzano, Laura and Panagou, Dimitra and Abate, Alessandro}, volume = {283}, series = {Proceedings of Machine Learning Research}, month = {04--06 Jun}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v283/main/assets/ziemann25b/ziemann25b.pdf}, url = {https://proceedings.mlr.press/v283/ziemann25b.html}, 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.} }
Endnote
%0 Conference Paper %T A Short Information-Theoretic Analysis of Linear Auto-Regressive Learning %A Ingvar Ziemann %B Proceedings of the 7th Annual Learning for Dynamics \& Control Conference %C Proceedings of Machine Learning Research %D 2025 %E Necmiye Ozay %E Laura Balzano %E Dimitra Panagou %E Alessandro Abate %F pmlr-v283-ziemann25b %I PMLR %P 26--30 %U https://proceedings.mlr.press/v283/ziemann25b.html %V 283 %X 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.
APA
Ziemann, I.. (2025). A Short Information-Theoretic Analysis of Linear Auto-Regressive Learning. Proceedings of the 7th Annual Learning for Dynamics \& Control Conference, in Proceedings of Machine Learning Research 283:26-30 Available from https://proceedings.mlr.press/v283/ziemann25b.html.

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