# Inverse Covariance and Partial Correlation Matrix Estimation via Joint Partial Regression

arXiv: https://arxiv.org/abs/2502.08414 · HTML: https://mlsanity.com/paper/2502.08414/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 5 of its 34 references that are in the map.
- First posted on arXiv 12 Feb 2025.

## Builds on (most cited first, 5 of 5)

- [A convex pseudo-likelihood framework for high dimensional partial correlation estimation with convergence guarantees](https://mlsanity.com/paper/1307.5381/) (2013)
- [A Tutorial on Regularized Partial Correlation Networks](https://mlsanity.com/paper/1607.01367/) (2016)
- [A new primal-dual algorithm for minimizing the sum of three functions with a linear operator](https://mlsanity.com/paper/1611.09805/) (2016)
- [Sparse Gaussian Graphical Models with Discrete Optimization: Computational and Statistical Perspectives](https://mlsanity.com/paper/2307.09366/) (2023)
- [Certifiably Optimal Sparse Inverse Covariance Estimation](https://mlsanity.com/paper/1906.10283/) (2019)

## Abstract (arXiv)

We present a method for estimating sparse high-dimensional inverse covariance and partial correlation matrices, which exploits the connection between the inverse covariance matrix and linear regression. The method is a two-stage estimation method wherein each individual feature is regressed on all other features while positive semi-definiteness is enforced simultaneously. We derive non-asymptotic estimation rates for both inverse covariance and partial correlation matrix estimation. An efficient proximal splitting algorithm for numerically computing the estimate is also dervied. The effectiveness of the proposed method is demonstrated on both synthetic and real-world data.