Partially Linear Additive Gaussian Graphical Models

Sinong Geng, Minhao Yan, Mladen Kolar, Sanmi Koyejo
Proceedings of the 36th International Conference on Machine Learning, PMLR 97:2180-2190, 2019.

Abstract

We propose a partially linear additive Gaussian graphical model (PLA-GGM) for the estimation of associations between random variables distorted by observed confounders. Model parameters are estimated using an $L_1$-regularized maximal pseudo-profile likelihood estimator (MaPPLE) for which we prove a $\sqrt{n}$-sparsistency. Importantly, our approach avoids parametric constraints on the effects of confounders on the estimated graphical model structure. Empirically, the PLA-GGM is applied to both synthetic and real-world datasets, demonstrating superior performance compared to competing methods.

Cite this Paper


BibTeX
@InProceedings{pmlr-v97-geng19a, title = {Partially Linear Additive {G}aussian Graphical Models}, author = {Geng, Sinong and Yan, Minhao and Kolar, Mladen and Koyejo, Sanmi}, booktitle = {Proceedings of the 36th International Conference on Machine Learning}, pages = {2180--2190}, year = {2019}, editor = {Kamalika Chaudhuri and Ruslan Salakhutdinov}, volume = {97}, series = {Proceedings of Machine Learning Research}, month = {09--15 Jun}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v97/geng19a/geng19a.pdf}, url = { http://proceedings.mlr.press/v97/geng19a.html }, abstract = {We propose a partially linear additive Gaussian graphical model (PLA-GGM) for the estimation of associations between random variables distorted by observed confounders. Model parameters are estimated using an $L_1$-regularized maximal pseudo-profile likelihood estimator (MaPPLE) for which we prove a $\sqrt{n}$-sparsistency. Importantly, our approach avoids parametric constraints on the effects of confounders on the estimated graphical model structure. Empirically, the PLA-GGM is applied to both synthetic and real-world datasets, demonstrating superior performance compared to competing methods.} }
Endnote
%0 Conference Paper %T Partially Linear Additive Gaussian Graphical Models %A Sinong Geng %A Minhao Yan %A Mladen Kolar %A Sanmi Koyejo %B Proceedings of the 36th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2019 %E Kamalika Chaudhuri %E Ruslan Salakhutdinov %F pmlr-v97-geng19a %I PMLR %P 2180--2190 %U http://proceedings.mlr.press/v97/geng19a.html %V 97 %X We propose a partially linear additive Gaussian graphical model (PLA-GGM) for the estimation of associations between random variables distorted by observed confounders. Model parameters are estimated using an $L_1$-regularized maximal pseudo-profile likelihood estimator (MaPPLE) for which we prove a $\sqrt{n}$-sparsistency. Importantly, our approach avoids parametric constraints on the effects of confounders on the estimated graphical model structure. Empirically, the PLA-GGM is applied to both synthetic and real-world datasets, demonstrating superior performance compared to competing methods.
APA
Geng, S., Yan, M., Kolar, M. & Koyejo, S.. (2019). Partially Linear Additive Gaussian Graphical Models. Proceedings of the 36th International Conference on Machine Learning, in Proceedings of Machine Learning Research 97:2180-2190 Available from http://proceedings.mlr.press/v97/geng19a.html .

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