# Joint Nonparametric Precision Matrix Estimation with Confounding

arXiv: https://arxiv.org/abs/1810.07147 · HTML: https://mlsanity.com/paper/1810.07147/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Oct 2018.

## Built on by (most cited first, 4 of 4)

- [An Adaptive Stochastic Sequential Quadratic Programming with Differentiable Exact Augmented Lagrangians](https://mlsanity.com/paper/2102.05320/) (2021)
- [SMILE: Evaluation and Domain Adaptation for Social Media Language Understanding](https://mlsanity.com/paper/2307.00135/) (2023)
- [Learning Gaussian Graphical Models with Latent Confounders](https://mlsanity.com/paper/2105.06600/) (2021)
- [Reinforcement Learning Paycheck Optimization for Multivariate Financial Goals](https://mlsanity.com/paper/2403.06011/) (2024)

## Abstract (arXiv)

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.