Capturing complex interactions among a large set of variables is a
challenging task. Probabilistic graphical models decouple these interactions into two parts, viz., structural or qualitative relationships represented by a graph, and parametric or quantitative relationships represented by values assigned to different groups of nodes. Graph estimation is an important task since it reveals useful relationships between the variables, but is challenging in high dimensions for loopy graphical models. Another important aspect that needs to be incorporated in modeling is the presence of latent or hidden variables.
In this talk, I will present models and methods for graph estimation in loopy graphical models with latent variables. I will give an overview of models and regimes, where graph estimation is tractable as well as present the strong theoretical guarantees proven for our proposed method. I will then present experimental outcome on newsgroup dataset, where it is seen that latent variables, corresponding to topics, are efficiently discovered, and incorporating loops in the model relaxes the requirement of a strict hierarchy between topics and words.