Joint Nonparametric Precision Matrix Estimation with Confounding

Sinong Geng, Mladen Kolar, Oluwasanmi Koyejo

Research output: Contribution to journalConference articlepeer-review


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 imaging (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, can be efficiently solved in parallel. Empirical results are presented using simulated and real brain imaging data and suggest that our approach improves precision matrix estimation as compared to baselines when confounding is present.

Original languageEnglish (US)
Pages (from-to)378-388
Number of pages11
JournalProceedings of Machine Learning Research
StatePublished - 2019
Externally publishedYes
Event35th Uncertainty in Artificial Intelligence Conference, UAI 2019 - Tel Aviv, Israel
Duration: Jul 22 2019Jul 25 2019

ASJC Scopus subject areas

  • Artificial Intelligence
  • Software
  • Control and Systems Engineering
  • Statistics and Probability


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