Learning High-Dimensional Differential Graphs From Multi-Attribute Data
Jitendra K Tugnait
We consider the problem of estimating differences in two Gaussian graphical
models (GGMs) which are known to have similar structure. The GGM structure is
encoded in its precision (inverse covariance) matrix. In many applications one
is interested in estimating the difference in two precision matrices to
characterize underlying changes in conditional dependencies of two sets of
data. Existing methods for differential graph estimation are based on
single-attribute (SA) models where one associates a scalar random variable with
each node. In multi-attribute (MA) graphical models, each node represents a
random vector. In this paper, we analyze a group lasso penalized D-trace loss
function approach for differential graph learning from multi-attribute data. An
alternating direction method of multipliers (ADMM) algorithm is presented to
optimize the objective function. Theoretical analysis establishing consistency
in support recovery and estimation in high-dimensional settings is provided.
Numerical results based on synthetic as well as real data are presented.