Graph Estimation From Multi-Attribute Data

摘要

Undirected graphical models are important in a number of modernapplications that involve exploring or exploiting dependencystructures underlying the data. For example, they are often usedto explore complex systems where connections between entitiesare not well understood, such as in functional brain networks orgenetic networks. Existing methods for estimating structure ofundirected graphical models focus on scenarios where each noderepresents a scalar random variable, such as a binary neuralactivation state or a continuous mRNA abundance measurement,even though in many real world problems, nodes can representmultivariate variables with much richer meanings, such as wholeimages, text documents, or multi-view feature vectors. In thispaper, we propose a new principled framework for estimating thestructure of undirected graphical models from such multivariate(or multi-attribute) nodal data. The structure of a graph isinferred through estimation of non-zero partial canonicalcorrelation between nodes. Under a Gaussian model, this strategyis equivalent to estimating conditional independencies betweenrandom vectors represented by the nodes and it generalizes theclassical problem of covariance selection (Dempster, 1972). Werelate the problem of estimating non-zero partial canonicalcorrelations to maximizing a penalized Gaussian likelihoodobjective and develop a method that efficiently maximizes thisobjective. Extensive simulation studies demonstrate theeffectiveness of the method under various conditions. We provideillustrative applications to uncovering gene regulatory networksfrom gene and protein profiles, and uncovering brainconnectivity graph from positron emission tomography data.Finally, we provide sufficient conditions under which the truegraphical structure can be recovered correctly. color="gray">