Generating Correlation Matrices with Graph Structures Using Convex Optimization

TL;DR

This paper introduces a convex optimization method for generating correlation matrices with specific sparsity patterns tied to graph structures, enabling more realistic data simulation and benchmarking of graph inference methods.

Contribution

It presents a novel convex optimization approach that controls the mean of entry distributions, improving flexibility over existing correlation matrix generation techniques.

Findings

Allows generation of correlation matrices with desired sparsity patterns

Provides better data realism for benchmarking statistical methods

Offers flexible control over entry distribution means

Abstract

This work deals with the generation of theoretical correlation matrices with specific sparsity patterns, associated to graph structures. We present a novel approach based on convex optimization, offering greater flexibility compared to existing techniques, notably by controlling the mean of the entry distribution in the generated correlation matrices. This allows for the generation of correlation matrices that better represent realistic data and can be used to benchmark statistical methods for graph inference.