Robust Estimation of Laplacian Constrained Gaussian Graphical Models with Trimmed Non-convex Regularization

Mariana Vargas Vieyra
Proceedings of The 11th International Conference on Probabilistic Graphical Models, PMLR 186:85-96, 2022.

Abstract

The problem of discovering a structure that fits a collection of vector data is of crucial importance for a variety of applications. Such problems can be framed as Laplacian con- strained Gaussian Graphical Model inference. Existing algorithms rely on the assumption that all the available observations are drawn from the same Multivariate Gaussian dis- tribution. However, in practice it is common to find scenarios where the datasets are contaminated with a certain number of outliers. The purpose of this work is to address that problem. We propose a robust method based on Trimmed Least Squares that copes with the presence of corrupted samples. We provide statistical guarantees on the estimation error and present results on both simulated data and real-world data.

Cite this Paper

BibTeX
@InProceedings{pmlr-v186-vargas-vieyra22a, title = {Robust Estimation of Laplacian Constrained Gaussian Graphical Models with Trimmed Non-convex Regularization}, author = {Vargas Vieyra, Mariana}, booktitle = {Proceedings of The 11th International Conference on Probabilistic Graphical Models}, pages = {85--96}, year = {2022}, editor = {Salmerón, Antonio and Rumı́, Rafael}, volume = {186}, series = {Proceedings of Machine Learning Research}, month = {05--07 Oct}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v186/vargas-vieyra22a/vargas-vieyra22a.pdf}, url = {https://proceedings.mlr.press/v186/vargas-vieyra22a.html}, abstract = {The problem of discovering a structure that fits a collection of vector data is of crucial importance for a variety of applications. Such problems can be framed as Laplacian con- strained Gaussian Graphical Model inference. Existing algorithms rely on the assumption that all the available observations are drawn from the same Multivariate Gaussian dis- tribution. However, in practice it is common to find scenarios where the datasets are contaminated with a certain number of outliers. The purpose of this work is to address that problem. We propose a robust method based on Trimmed Least Squares that copes with the presence of corrupted samples. We provide statistical guarantees on the estimation error and present results on both simulated data and real-world data.} }
Endnote
%0 Conference Paper %T Robust Estimation of Laplacian Constrained Gaussian Graphical Models with Trimmed Non-convex Regularization %A Mariana Vargas Vieyra %B Proceedings of The 11th International Conference on Probabilistic Graphical Models %C Proceedings of Machine Learning Research %D 2022 %E Antonio Salmerón %E Rafael Rumı́ %F pmlr-v186-vargas-vieyra22a %I PMLR %P 85--96 %U https://proceedings.mlr.press/v186/vargas-vieyra22a.html %V 186 %X The problem of discovering a structure that fits a collection of vector data is of crucial importance for a variety of applications. Such problems can be framed as Laplacian con- strained Gaussian Graphical Model inference. Existing algorithms rely on the assumption that all the available observations are drawn from the same Multivariate Gaussian dis- tribution. However, in practice it is common to find scenarios where the datasets are contaminated with a certain number of outliers. The purpose of this work is to address that problem. We propose a robust method based on Trimmed Least Squares that copes with the presence of corrupted samples. We provide statistical guarantees on the estimation error and present results on both simulated data and real-world data.
APA
Vargas Vieyra, M.. (2022). Robust Estimation of Laplacian Constrained Gaussian Graphical Models with Trimmed Non-convex Regularization. Proceedings of The 11th International Conference on Probabilistic Graphical Models, in Proceedings of Machine Learning Research 186:85-96 Available from https://proceedings.mlr.press/v186/vargas-vieyra22a.html.

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