On Learning Continuous Pairwise Markov Random Fields

Abhin Shah, Devavrat Shah, Gregory Wornell
Proceedings of The 24th International Conference on Artificial Intelligence and Statistics, PMLR 130:1153-1161, 2021.

Abstract

We consider learning a sparse pairwise Markov Random Field (MRF) with continuous-valued variables from i.i.d samples. We adapt the algorithm of Vuffray et al. (2019) to this setting and provide finite-sample analysis revealing sample complexity scaling logarithmically with the number of variables, as in the discrete and Gaussian settings. Our approach is applicable to a large class of pairwise MRFs with continuous variables and also has desirable asymptotic properties, including consistency and normality under mild conditions. Further, we establish that the population version of the optimization criterion employed in Vuffray et al. (2019) can be interpreted as local maximum likelihood estimation (MLE). As part of our analysis, we introduce a robust variation of sparse linear regression a‘ la Lasso, which may be of interest in its own right.

Cite this Paper

BibTeX
@InProceedings{pmlr-v130-shah21a, title = { On Learning Continuous Pairwise Markov Random Fields }, author = {Shah, Abhin and Shah, Devavrat and Wornell, Gregory}, booktitle = {Proceedings of The 24th International Conference on Artificial Intelligence and Statistics}, pages = {1153--1161}, year = {2021}, editor = {Banerjee, Arindam and Fukumizu, Kenji}, volume = {130}, series = {Proceedings of Machine Learning Research}, month = {13--15 Apr}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v130/shah21a/shah21a.pdf}, url = {https://proceedings.mlr.press/v130/shah21a.html}, abstract = { We consider learning a sparse pairwise Markov Random Field (MRF) with continuous-valued variables from i.i.d samples. We adapt the algorithm of Vuffray et al. (2019) to this setting and provide finite-sample analysis revealing sample complexity scaling logarithmically with the number of variables, as in the discrete and Gaussian settings. Our approach is applicable to a large class of pairwise MRFs with continuous variables and also has desirable asymptotic properties, including consistency and normality under mild conditions. Further, we establish that the population version of the optimization criterion employed in Vuffray et al. (2019) can be interpreted as local maximum likelihood estimation (MLE). As part of our analysis, we introduce a robust variation of sparse linear regression a‘ la Lasso, which may be of interest in its own right. } }
Endnote
%0 Conference Paper %T On Learning Continuous Pairwise Markov Random Fields %A Abhin Shah %A Devavrat Shah %A Gregory Wornell %B Proceedings of The 24th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2021 %E Arindam Banerjee %E Kenji Fukumizu %F pmlr-v130-shah21a %I PMLR %P 1153--1161 %U https://proceedings.mlr.press/v130/shah21a.html %V 130 %X We consider learning a sparse pairwise Markov Random Field (MRF) with continuous-valued variables from i.i.d samples. We adapt the algorithm of Vuffray et al. (2019) to this setting and provide finite-sample analysis revealing sample complexity scaling logarithmically with the number of variables, as in the discrete and Gaussian settings. Our approach is applicable to a large class of pairwise MRFs with continuous variables and also has desirable asymptotic properties, including consistency and normality under mild conditions. Further, we establish that the population version of the optimization criterion employed in Vuffray et al. (2019) can be interpreted as local maximum likelihood estimation (MLE). As part of our analysis, we introduce a robust variation of sparse linear regression a‘ la Lasso, which may be of interest in its own right.
APA
Shah, A., Shah, D. & Wornell, G.. (2021). On Learning Continuous Pairwise Markov Random Fields . Proceedings of The 24th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 130:1153-1161 Available from https://proceedings.mlr.press/v130/shah21a.html.

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