Department of Statistics -statistics Seminar – Fall 2014 Tingting Zhang (university of Virginia) " a Dynamic Directional Model for Effective Brain Connectivity Using Electrocorticographic (ecog) Time Series " "fiber Direction Estimation in Diffusion Mri"

Projections of countries' future populations, broken down by age and sex, are widely used for planning and research. They are mostly done deterministically, but there is a widespread need for probabilistic projections. I will describe a Bayesian statistical method for probabilistic population projections for all countries. These new methods have been used by the United Nations to produce their most recent population projections for all countries. 10/27/2014 Venkat Chandrasekaharn (Caltech) Title: Latent Variable Graphical Model Selection via Convex Optimization Suppose we have a Gaussian graphical model with sample observations ofonly a subset of the variables. Can we separate the extra correlations induced due to marginalization over the unobserved, hidden variables from the structure among the observed variables? In other words is it still possible to consistently perform model selection despite the unobserved, latent variables? As we shall see the key problem that arises is one of decomposing the concentration matrix of the observed variables into a sparse matrix (representing graphical model structure among the observed variables) and a low rank matrix (representing the effects of marginalization over the hidden variables). Such a decomposition can be accomplished by an estimator that is given by a tractable convex program. This estimator performs consistent model selection in the high-dimensional scaling regime in which the number of observed/hidden variables grows with the number of samples of the observed variables. The geometric aspects of our approach are highlighted, with the algebraic varieties of sparse matrices and of low rank matrices playing an important role. Bio: Venkat Chandrasekaran is an Assistant Professor at Caltech in Computing and Mathematical Sciences and in Electrical Engineering. He received a Ph.D. in Electrical Engineering and Computer Science in June 2011 from MIT, and he received a B.A. in Mathematics as well as a B.S. in Electrical and Computer Engineering in May 2005 from Rice University. He was awarded the Jin-Au Kong Dissertation Prize for the best doctoral thesis in Electrical Engineering at MIT (2012), the Young Researcher Prize in Continuous Optimization at the Fourth International Conference on Continuous Optimization of the Mathematical Optimization Society (2013, awarded once every three years), an Okawa Research Grant in Information and Telecommunications (2013), and an NSF CAREER award (2014). His research interests lie in mathematical optimization and its application to the information sciences.