Graph Estimation From Multi-attribute Data

TL;DR

This paper introduces a novel framework for estimating graphs from multi-attribute data, using partial canonical correlations to handle complex nodal features, with theoretical guarantees and practical applications in biology and neuroscience.

Contribution

The paper proposes a new method for graph estimation from multi-attribute data using partial canonical correlations, along with an efficient algorithm and theoretical consistency guarantees.

Findings

Method accurately recovers graphs in simulations.

Successfully applied to gene regulatory network inference.

Effectively uncovers brain connectivity from fMRI data.

Abstract

Many real world network problems often concern multivariate nodal attributes such as image, textual, and multi-view feature vectors on nodes, rather than simple univariate nodal attributes. The existing graph estimation methods built on Gaussian graphical models and covariance selection algorithms can not handle such data, neither can the theories developed around such methods be directly applied. In this paper, we propose a new principled framework for estimating graphs from multi-attribute data. Instead of estimating the partial correlation as in current literature, our method estimates the partial canonical correlations that naturally accommodate complex nodal features. Computationally, we provide an efficient algorithm which utilizes the multi-attribute structure. Theoretically, we provide sufficient conditions which guarantee consistent graph recovery. Extensive simulation studies demonstrate performance of our method under various conditions. Furthermore, we provide illustrative applications to uncovering gene regulatory networks from gene and protein profiles, and uncovering brain connectivity graph from functional magnetic resonance imaging data.