Inconsistency of Cross-Validation for Structure Learning in Gaussian Graphical Models

Zhao Lyu, Wai Ming Tai, Mladen Kolar, Bryon Aragam
Proceedings of The 27th International Conference on Artificial Intelligence and Statistics, PMLR 238:3691-3699, 2024.

Abstract

Despite numerous years of research into the merits and trade-offs of various model selection criteria, obtaining robust results that elucidate the behavior of cross-validation remains a challenging endeavor. In this paper, we highlight the inherent limitations of cross-validation when employed to discern the structure of a Gaussian graphical model. We provide finite-sample bounds on the probability that the Lasso estimator for the neighborhood of a node within a Gaussian graphical model, optimized using a prediction oracle, misidentifies the neighborhood. Our results pertain to both undirected and directed acyclic graphs, encompassing general, sparse covariance structures. To support our theoretical findings, we conduct an empirical investigation of this inconsistency by contrasting our outcomes with other commonly used information criteria through an extensive simulation study. Given that many algorithms designed to learn the structure of graphical models require hyperparameter selection, the precise calibration of this hyperparameter is paramount for accurately estimating the inherent structure. Consequently, our observations shed light on this widely recognized practical challenge.

Cite this Paper

BibTeX
@InProceedings{pmlr-v238-lyu24a, title = { Inconsistency of Cross-Validation for Structure Learning in {G}aussian Graphical Models }, author = {Lyu, Zhao and Ming Tai, Wai and Kolar, Mladen and Aragam, Bryon}, booktitle = {Proceedings of The 27th International Conference on Artificial Intelligence and Statistics}, pages = {3691--3699}, year = {2024}, editor = {Dasgupta, Sanjoy and Mandt, Stephan and Li, Yingzhen}, volume = {238}, series = {Proceedings of Machine Learning Research}, month = {02--04 May}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v238/lyu24a/lyu24a.pdf}, url = {https://proceedings.mlr.press/v238/lyu24a.html}, abstract = { Despite numerous years of research into the merits and trade-offs of various model selection criteria, obtaining robust results that elucidate the behavior of cross-validation remains a challenging endeavor. In this paper, we highlight the inherent limitations of cross-validation when employed to discern the structure of a Gaussian graphical model. We provide finite-sample bounds on the probability that the Lasso estimator for the neighborhood of a node within a Gaussian graphical model, optimized using a prediction oracle, misidentifies the neighborhood. Our results pertain to both undirected and directed acyclic graphs, encompassing general, sparse covariance structures. To support our theoretical findings, we conduct an empirical investigation of this inconsistency by contrasting our outcomes with other commonly used information criteria through an extensive simulation study. Given that many algorithms designed to learn the structure of graphical models require hyperparameter selection, the precise calibration of this hyperparameter is paramount for accurately estimating the inherent structure. Consequently, our observations shed light on this widely recognized practical challenge. } }
Endnote
%0 Conference Paper %T Inconsistency of Cross-Validation for Structure Learning in Gaussian Graphical Models %A Zhao Lyu %A Wai Ming Tai %A Mladen Kolar %A Bryon Aragam %B Proceedings of The 27th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2024 %E Sanjoy Dasgupta %E Stephan Mandt %E Yingzhen Li %F pmlr-v238-lyu24a %I PMLR %P 3691--3699 %U https://proceedings.mlr.press/v238/lyu24a.html %V 238 %X Despite numerous years of research into the merits and trade-offs of various model selection criteria, obtaining robust results that elucidate the behavior of cross-validation remains a challenging endeavor. In this paper, we highlight the inherent limitations of cross-validation when employed to discern the structure of a Gaussian graphical model. We provide finite-sample bounds on the probability that the Lasso estimator for the neighborhood of a node within a Gaussian graphical model, optimized using a prediction oracle, misidentifies the neighborhood. Our results pertain to both undirected and directed acyclic graphs, encompassing general, sparse covariance structures. To support our theoretical findings, we conduct an empirical investigation of this inconsistency by contrasting our outcomes with other commonly used information criteria through an extensive simulation study. Given that many algorithms designed to learn the structure of graphical models require hyperparameter selection, the precise calibration of this hyperparameter is paramount for accurately estimating the inherent structure. Consequently, our observations shed light on this widely recognized practical challenge.
APA
Lyu, Z., Ming Tai, W., Kolar, M. & Aragam, B.. (2024). Inconsistency of Cross-Validation for Structure Learning in Gaussian Graphical Models . Proceedings of The 27th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 238:3691-3699 Available from https://proceedings.mlr.press/v238/lyu24a.html.

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