Dr. Caiyan Li : Statistical Methods for Analysis of Graph constrained Genomic data

Posted by Min Yang , part of the Statistics and Data Science Seminar.

At

Sept. 11, 2013, 4 p.m.

In

SEO 636

Abstract

Graphs and networks are common ways of depicting biological information. In biology, many different biological processes are represented by graphs, such as regulatory networks, metabolic pathways and protein protein interaction networks. This kind of a priori use of graphs is a useful supplement to the standard numerical data such as microarray gene expression data. In this presentation, we consider the problem of regression analysis and variable selection when the covariates are linked on a graph. We study a graph constrained regularization procedure and its theoretical properties for regression analysis to take into account the neighborhood information of the variables measured on a graph. This procedure involves a smoothness penalty on the coefficients that is defined as a quadratic form of the Laplacian matrix associated with the graph. We establish estimation and model selection consistency results and provide estimation bounds for both fixed and diverging numbers of parameters in regression models. We also developed a second method using Markov Random Field to incorporate the graph information into analysis of high dimensional data. Finally, we demonstrate by simulations and a real dataset that the proposed procedure can lead to better variable selection and prediction than existing methods that ignore the graph information associated with the covariates.