Statistics Seminar: STA 290
Thursday, April 4th , 2013 at 4:10pm, MSB 1147 (Colloquium Room)
Refreshments at 3:30pm in MSB 4110 (Statistics Lounge)
Speaker: Andrew B. Nobel, Department of Statistics and Operations Research, Univ. North Carolina at Chapel Hill
Title: "Large Average Submatrices of a Gaussian Random Matrix: Landscapes and Local Optima"
Abstract: The problem of finding large average submatrices of a real-valued matrix is a data mining problem that 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 will begin by considering the average and joint distribution of the k x k submatrix having largest average value (the global maximum). We will then turn our attention to submatrices with dominant row and column sums, which arise as the local maxima of a practical iterative search procedure. We characterize the value and joint distribution of a local maximum, and show that a typical local maxima has an average value within a constant factor of the global maximum. In the last part of the talk we will consider the *number* L_n(k) of k x k local maxima, 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)