Inverse Covariance and Partial Correlation Matrix Estimation via Joint Partial Regression

Fuente: arXiv
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Autores principales: Erickson, Samuel, Rydén, Tobias
Formato: Preprint
Publicado: 2025
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author Erickson, Samuel
Rydén, Tobias
author_facet Erickson, Samuel
Rydén, Tobias
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2502_08414
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Inverse Covariance and Partial Correlation Matrix Estimation via Joint Partial Regression
Erickson, Samuel
Rydén, Tobias
Machine Learning
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.
title Inverse Covariance and Partial Correlation Matrix Estimation via Joint Partial Regression
topic Machine Learning
url https://arxiv.org/abs/2502.08414