ISE SEMINAR SERIES

Title: Learning with difference-of-convex sparsity functions

Speaker: Miju Ahn, Southern Methodist University

Time & Location:

Abstract      

Variable selection is a fundamental methodology in statistical learning performed to obtain sparse representation of the trained model parameters. The first part of this talk emphasizes on studying properties of stationary solutions of the learning formulations where sparsity functions are used in the objective function. We derive bounds for the distance between the stationary solutions and a vector that is possibly the ground truth, and the model predictions produced by them. Furthermore, the inclusion relationships between their support sets are studied. Some of the results are generalization of the existing theory shown for the L1-norm regularized least squares minimization problem. The second part emphasizes on the constraint system defined by the sparsity functions. A system of affine sparsity constraints (ASCs) formulates various logical conditions among the variables as hard constraints. Structural properties of the set including its closeness and the characterization of its closure are analyzed. The set convergence of the approximation sets to the set of ASCs is presented.

Bio sketch

Miju Ahn is an Assistant Professor in the Department of Engineering Management, Information, and Systems (EMIS) of the Lyle School of Engineering at the Southern Methodist University. She received her Ph.D. in Industrial and Systems Engineering from University of Southern California. For undergraduate studies, she received B.A. in Applied Mathematics and obtained Industrial Engineering and Operations Research (IEOR) minor at University of California, Berkeley. Her research interests include computational optimization, operations research, statistical/machine learning, and big-data science.