Alfred Hero, R. Jamison and Betty Williams Professor of Engineering
University of Michigan
Correlation graphs arise in many areas of engineering, social science, and natural science where they are used to explore the dependency structure. In this talk we will present recent results on screening correlation graphs for connectivity patterns when the graph is constructed from sample correlations with a small number of observations. As the number of variables increases screening for connected variables becomes futile due to a high dimensional phase transition phenomenon: with high probability most variables will have large sample correlations even when there is no correlation present. We apply our framework to the problem of hub discovery in correlation and partial correlation (concentration) graphs. We illustrate our correlation screening framework in computational biology and, in particular, for discovery of influential variables in gene regulation networks. This is joint work with Bala Rajaratnam at Stanford University.
Alfred Hero is the R. Jamison and Betty Williams Professor of Engineering at the University of Michigan. He also holds the position of Digiteo Chair at the Digiteo Research Institute in France. At the University of Michigan his primary appointment is in the Department of Electrical Engineering and Computer Science (EECS) and he has secondary appointments in the Department of Biomedical Engineering and the Department of Statistics. He is also affiliated with the UM Program in Biomedical Science (PIBS) and the UM Graduate Program in Applied and Interdisciplinary Mathematics (AIM).