Soledad Villar: Classification-aware dimensionality reduction and genetic marker selection

Abstract: Classification and dimensionality reduction are two fundamental problems in mathematical data science. Given labeled points in a high-dimensional vector space, we seek a projection onto a low dimensional subspace that maintains the classification structure of the data. Taking inspiration from large margin nearest neighbor classification, this work introduces SqueezeFit, a semidefinite relaxation of this problem. Unlike its predecessors, this relaxation is amenable to theoretical analysis, allowing us to provably recover a planted projection operator from the data. An ongoing collaboration considers a linear program version of SqueezeFit that identifies the markers in genetic data that preserve the classification structure of single-cell RNA sequencing data.Short Bio: Soledad Villar is a Moore-Sloan Research Fellow at the NYU Center for Data Science. She is also currently affiliated to the Courant Institute of Mathematical Sciences and the Simons Collaboration Algorithms and Geometry. In 2017 Soledad received her PhD in Mathematics from the University of Texas at Austin and spent the following fall as a research fellow at University of California at Berkeley. Her research is in mathematical data science. She uses optimization, statistics, machine learning, applied harmonic analysis and geometric tools to address fundamental mathematical questions that arise from data-related problems in scientific applications. Before coming to the U.S., Soledad conducted her undergraduate and masters studies in her home country, Uruguay.