IST LUNCH BUNCH

Graphical model is a probabilistic model for which a graph is used to represent the conditional independence between random variables. Such models have become extremely popular tools for modeling complex real-world systems. Learning graphical models is of fundamental importance in machine learning and statistics and is often challenged by the fact that only a small number of samples are available relative to the number of variables. Several methods (such as Graphical Lasso) have been proposed to address this problem. However, there is a glaring lack of concrete case studies that clearly illustrate the limitations of the existing computational methods for learning graphical models. In this talk, I will propose a circuit model that can be used as a platform for testing the performance of different statistical approaches. I will also develop new insights into regularized semidefinite program (SDP) problems by working through the Graphical Lasso algorithm. Graphical Lasso is a popular method for learning the structure of a Gaussian model, which relies on solving a computationally-expensive SDP. I will derive sufficient conditions under which the solution of this large-scale SDP has a simple formula. I will illustrates our results on electrical circuits and fMRI data for finding brain networks.