Joint Nonparametric Precision Matrix Estimation with Confounding

Sinong Geng, Mladen Kolar, Oluwasanmi Koyejo
Proceedings of The 35th Uncertainty in Artificial Intelligence Conference, PMLR 115:378-388, 2020.

Abstract

We consider the problem of precision matrix estimation where, due to extraneous confounding of the underlying precision matrix, the data are independent but not identically distributed. While such confounding occurs in many scientific problems, our approach is inspired by recent neuroscientific research suggesting that brain function, as measured using functional magnetic resonance imagine (fMRI), is susceptible to confounding by physiological noise such as breathing and subject motion. Following the scientific motivation, we propose a graphical model, which in turn motivates a joint nonparametric estimator. We provide theoretical guarantees for the consistency and the convergence rate of the proposed estimator. In addition, we demonstrate that the optimization of the proposed estimator can be transformed into a series of linear programming problems, and thus be efficiently solved in parallel. Empirical results are presented using simulated and real brain imaging data, which suggest that our approach improves precision matrix estimation, as compared to baselines, when confounding is present.

Cite this Paper

BibTeX
@InProceedings{pmlr-v115-geng20a, title = {Joint Nonparametric Precision Matrix Estimation with Confounding}, author = {Geng, Sinong and Kolar, Mladen and Koyejo, Oluwasanmi}, booktitle = {Proceedings of The 35th Uncertainty in Artificial Intelligence Conference}, pages = {378--388}, year = {2020}, editor = {Adams, Ryan P. and Gogate, Vibhav}, volume = {115}, series = {Proceedings of Machine Learning Research}, month = {22--25 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v115/geng20a/geng20a.pdf}, url = {https://proceedings.mlr.press/v115/geng20a.html}, abstract = {We consider the problem of precision matrix estimation where, due to extraneous confounding of the underlying precision matrix, the data are independent but not identically distributed. While such confounding occurs in many scientific problems, our approach is inspired by recent neuroscientific research suggesting that brain function, as measured using functional magnetic resonance imagine (fMRI), is susceptible to confounding by physiological noise such as breathing and subject motion. Following the scientific motivation, we propose a graphical model, which in turn motivates a joint nonparametric estimator. We provide theoretical guarantees for the consistency and the convergence rate of the proposed estimator. In addition, we demonstrate that the optimization of the proposed estimator can be transformed into a series of linear programming problems, and thus be efficiently solved in parallel. Empirical results are presented using simulated and real brain imaging data, which suggest that our approach improves precision matrix estimation, as compared to baselines, when confounding is present.} }
Endnote
%0 Conference Paper %T Joint Nonparametric Precision Matrix Estimation with Confounding %A Sinong Geng %A Mladen Kolar %A Oluwasanmi Koyejo %B Proceedings of The 35th Uncertainty in Artificial Intelligence Conference %C Proceedings of Machine Learning Research %D 2020 %E Ryan P. Adams %E Vibhav Gogate %F pmlr-v115-geng20a %I PMLR %P 378--388 %U https://proceedings.mlr.press/v115/geng20a.html %V 115 %X We consider the problem of precision matrix estimation where, due to extraneous confounding of the underlying precision matrix, the data are independent but not identically distributed. While such confounding occurs in many scientific problems, our approach is inspired by recent neuroscientific research suggesting that brain function, as measured using functional magnetic resonance imagine (fMRI), is susceptible to confounding by physiological noise such as breathing and subject motion. Following the scientific motivation, we propose a graphical model, which in turn motivates a joint nonparametric estimator. We provide theoretical guarantees for the consistency and the convergence rate of the proposed estimator. In addition, we demonstrate that the optimization of the proposed estimator can be transformed into a series of linear programming problems, and thus be efficiently solved in parallel. Empirical results are presented using simulated and real brain imaging data, which suggest that our approach improves precision matrix estimation, as compared to baselines, when confounding is present.
APA
Geng, S., Kolar, M. & Koyejo, O.. (2020). Joint Nonparametric Precision Matrix Estimation with Confounding. Proceedings of The 35th Uncertainty in Artificial Intelligence Conference, in Proceedings of Machine Learning Research 115:378-388 Available from https://proceedings.mlr.press/v115/geng20a.html.

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