# Joint Estimation of Precision Matrices in Heterogeneous Populations

arXiv: https://arxiv.org/abs/1601.00142 · HTML: https://mlsanity.com/paper/1601.00142/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Jan 2016.

## Built on by (most cited first, 5 of 5)

- [Joint Gaussian Graphical Model Estimation: A Survey](https://mlsanity.com/paper/2110.10281/) (2021)
- [Trans-Glasso: A Transfer Learning Approach to Precision Matrix Estimation](https://mlsanity.com/paper/2411.15624/) (2024)
- [Joint Estimation and Inference for Multi-Experiment Networks of High-Dimensional Point Processes](https://mlsanity.com/paper/2109.11634/) (2021)
- [Efficient Inference of Spatially-varying Gaussian Markov Random Fields with Applications in Gene Regulatory Networks](https://mlsanity.com/paper/2206.10174/) (2022)
- [Joint learning of multiple Granger causal networks via non-convex regularizations: Inference of group-level brain connectivity](https://mlsanity.com/paper/2105.07196/) (2021)

## Abstract (arXiv)

We introduce a general framework for estimation of inverse covariance, or precision, matrices from heterogeneous populations. The proposed framework uses a Laplacian shrinkage penalty to encourage similarity among estimates from disparate, but related, subpopulations, while allowing for differences among matrices. We propose an efficient alternating direction method of multipliers (ADMM) algorithm for parameter estimation, as well as its extension for faster computation in high dimensions by thresholding the empirical covariance matrix to identify the joint block diagonal structure in the estimated precision matrices. We establish both variable selection and norm consistency of the proposed estimator for distributions with exponential or polynomial tails. Further, to extend the applicability of the method to the settings with unknown populations structure, we propose a Laplacian penalty based on hierarchical clustering, and discuss conditions under which this data-driven choice results in consistent estimation of precision matrices in heterogenous populations. Extensive numerical studies and applications to gene expression data from subtypes of cancer with distinct clinical outcomes indicate the potential advantages of the proposed method over existing approaches.