CCSP Seminar: Radu Balan, "Low-Rank Matrix Estimation and Rank-one Matrix Decompositions"
Communication, Control and Signal Processing Seminar
Low-Rank Matrix Estimation and Rank-one Matrix Decompositions
Department of Mathematics and CSCAMM
University of Maryland
Abstract: In this talk, we present two points of view to broad classes of inverse problems: Lipschitz inversion and Cramer-Rao Lower Bounds. Given a nonlinear transformation of some data (e.g. incomplete observations of a low-rank matrix, or measurements of magnitudes of a linear transform) one is presented with the problem of stable inversion of this transformation. In this talk we are interested in finding fundamental lower bounds of any algorithm. We shall discuss the concept of Lipschitz retract and a universal class of signal estimators (Whitney-McShaun-Kirszbraun). Then we formulate the same problem from a frequentist statistical estimation perspective, and discuss the associated CRL bound.
If time permits we discuss also a special matrix decomposition problem inspired by expansions of integral operators on modulation spaces. Here we seek a decomposition of the covariance matrix into a sum of rank-one matrices that minimize an l1-type penalty.