  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.
