# A Proximal Distance Algorithm for Likelihood-Based Sparse Covariance Estimation

arXiv: https://arxiv.org/abs/2109.04497 · HTML: https://mlsanity.com/paper/2109.04497/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Sep 2021.

## Built on by (most cited first, 3 of 3)

- [Bayesian Transfer Learning](https://mlsanity.com/paper/2312.13484/) (2023)
- [The Stochastic Proximal Distance Algorithm](https://mlsanity.com/paper/2210.12277/) (2022)
- [Inertial Quadratic Majorization Minimization with Application to Kernel Regularized Learning](https://mlsanity.com/paper/2507.04247/) (2025)

## Abstract (arXiv)

This paper addresses the task of estimating a covariance matrix under a patternless sparsity assumption. In contrast to existing approaches based on thresholding or shrinkage penalties, we propose a likelihood-based method that regularizes the distance from the covariance estimate to a symmetric sparsity set. This formulation avoids unwanted shrinkage induced by more common norm penalties and enables optimization of the resulting non-convex objective by solving a sequence of smooth, unconstrained subproblems. These subproblems are generated and solved via the proximal distance version of the majorization-minimization principle. The resulting algorithm executes rapidly, gracefully handles settings where the number of parameters exceeds the number of cases, yields a positive definite solution, and enjoys desirable convergence properties. Empirically, we demonstrate that our approach outperforms competing methods by several metrics across a suite of simulated experiments. Its merits are illustrated on an international migration dataset and a classic case study on flow cytometry. Our findings suggest that the marginal and conditional dependency networks for the cell signalling data are more similar than previously concluded.