Graph Estimation From Multi-attribute 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.

Extended simulation study. Added an application to a new data set

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• Brain covariance selection: better individual functional connectivity models using population prior
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Cited by in corpus (6)

• On Sparse High-Dimensional Graphical Model Learning For Dependent Time Series
• Inter-Subject Analysis: Inferring Sparse Interactions with Dense Intra-Graphs
• Learning High-Dimensional Differential Graphs From Multi-Attribute Data
• Joint Nonparametric Precision Matrix Estimation with Confounding
• Multivariate Gaussian Network Structure Learning
• Multi-Attribute Graph Estimation with Sparse-Group Non-Convex Penalties