This week's Statistics Seminar speaker will be Andrew Nobel from UNC Chapel Hill.
Talk Title: Large Average Submatrices of a Gaussian Random Matrix: Landscapes and Local Optima
The problem of finding large average submatrices of a real-valued matrix arises in the exploratory analysis of data from disciplines as diverse as genomics and social sciences. This talk presents several new results concerning large average submatrices of an n x n Gaussian random matrix. We begin by considering the average and joint distribution of the k x k submatrix having largest average value (global optimum). We then turn our attention to submatrices with dominant row and column sums, which arise as the local optima of a practical iterative search procedure. We characterize the joint distribution of a local optimum, and show that a typical local optima has an average value within a constant factor of the global optimum. In the last part of the talk we consider the *number* L_n(k) of locally optimal kxk submatices, beginning with the asymptotic behavior of its mean and variance for fixed k and increasing n. Finally, we present a central limit theorem for L_n(k) that is based on Stein's method for normal approximation.
Joint work with Shankar Bhamidi (UNC) and Partha S. Dey (Courant).
Refreshments will be served after the seminar in 1181 Comstock Hall.