Title:Extracting correlation structure from large random matrices
Abstract: Random matrices arise in many areas of engineering, social sciences,
and natural sciences. For example, when rows of the random matrix
record successive samples of a multivariate response the sample
correlation between the columns can reveal important dependency
structure in the multivariate response, e.g., stars, hubs and triangles
of codependency. However, when the number of samples is finite and
the number p of columns increases such exploration
becomes futile due to a phase transition phenomenon: spurious
discoveries will eventually dominate. In this
presentation I will present theory for predicting these phase
transitions and present Poisson limit theorems that
can be used to predict finite sample behavior of correlation structure. The theory has application
to areas including gene expression analysis, remote sensing, and portfolio selection.
This is joint work Bala Rajaratnam.
