Joint Nonparametric Precision Matrix Estimation with Confounding

TL;DR

This paper introduces a joint nonparametric method for estimating precision matrices in the presence of confounding factors, with theoretical guarantees and efficient optimization, demonstrated on brain imaging data.

Contribution

It proposes a novel graphical model and estimator that handle confounding in precision matrix estimation, with proven consistency and scalable optimization.

Findings

Improved accuracy over baselines in simulated data

Effective correction of confounding in brain imaging data

Theoretical guarantees for estimator consistency

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.