Dr. Anindya Roy, UMBC

Title: Some Properties of Correlation Matrices and Their Application

Abstract:

I will discuss mostly known properties of correlation matrices but use them in two new applications. The first one is in data privacy where the problem of interest can be posed as a problem of sampling from a scale mixture with linear equality constraints. The second application is in meta-analysis where the question of interest is a correlation matrix completion problem with a known missingness mechanism. Both problems require correlation matrices that are nearest to given matrices. I will give new proof of a necessary and sufficient condition for a vector to be a null vector of a correlation matrix. The talk is mostly for graduate students as I will discuss different known results from matrix completion/alternating projection algorithm and graphical models. The work is joint with Ryan Lafferty and is a part of his dissertation.