November 18, 2014, 4:00pm
Daniela Witten, Departments of Biostatistics and Statistics, UW.
Flexible Graphical Modeling
Abstract: In recent years, there has been considerable interest in estimating conditional dependence relationships among random variables in the high-dimensional setting, in which the number of variables far exceeds the number of available observations. Most prior work has assumed that the variables are multivariate Gaussian, or that the conditional means of the variables are linear. Unfortunately, if these assumptions are violated, then the resulting estimates can be inaccurate.
I will present two recent lines of work on learning the conditional dependence graph of a set of random variables in the non-Gaussian setting. First, I will present a semi-parametric method that allows the conditional means of the features to take on an arbitrary additive form. Next, I will present an approach for learning a graph in which the distribution of each node, conditioned on the others, may have a different parametric form. Each approach is formulated as the solution to a convex optimization problem corresponding to a penalized log likelihood.
This is joint work with Ali Shojaie, Shizhe Chen, and Arend Voorman.