Karthik Mohan; Structured Learning of Gaussian Graphical Models

January 22, 2013, 4:00pm
Karthik Mohan, Department of Electrical Engineering, University of Washington.

Abstract: We consider the problem of estimating multiple gaussian graphical models given data in the high-dimensional setting and also given structured prior knowledge on the how the models interact with each other. This problem has applications in computational biology, social networks, etc. To encourage the structured learning of graphical models, we construct a regularizer based on group sparsity, called the structured overlap norm. The regularizer is then used to construct a family of optimization problems which when solved, promote graphical models with the desired structure. To solve the resulting set of optimization problems, we propose to use the ADMM algorithm. Standard first order methods such as the sub-gradient method, proximal-gradient method, etc are inefficient due to the structure of our regularizer. We also develop a set of necessary and sufficient conditions for the optimal solution to have a block-diagonal structure. This enables breaking down the optimization problem into multiple sub-problems leading to significant gains in computation without loss of accuracy. Finally, we present some preliminary numerical results that show that the solution to the optimization problem does indeed promote graphical models with the desired structure.

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