Joint Nonparametric Precision Matrix Estimation with Confounding
This work addresses confounding in precision matrix estimation, particularly for neuroscience applications like fMRI analysis, but it appears incremental as it builds on existing graphical models and nonparametric methods.
The paper tackles the problem of precision matrix estimation in the presence of extraneous confounding, such as physiological noise in fMRI data, by proposing a joint nonparametric estimator. Empirical results show that this approach improves estimation compared to baselines when confounding is present.
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.