[Ml-stat-talks] Princeton Optimization Seminar - Po-Ling Loh, UPenn, March 26
Amir Ali Ahmadi
a_a_a at princeton.edu
Thu Mar 19 10:18:35 EDT 2015
----- Princeton Optimization Seminar -----
DATE: Thursday, March 26 2015
TIME: 4:30 pm
LOCATION: Sherrerd Hall 101
SPEAKER: Po-Ling Loh, University of Pennsylvania
TITLE: PDW Methods for Support Recovery in Nonconvex High-dimensional Problems
The primal-dual witness (PDW) technique is a now-standard proof strategy for establishing variable selection consistency for sparse high-dimensional estimation problems when the objective function and regularizer are convex. The method proceeds by optimizing the objective function over the parameter space restricted to the true support of the unknown vector, then using a dual witness to certify that the resulting solution is also a global optimum of the unrestricted problem. We present a modified primal-dual witness framework that may be applied even to nonconvex, penalized objective functions that satisfy certain regularity conditions. Notably, our theory allows us to derive rigorous support recovery guarantees for local and global optima of regularized regression estimators involving nonconvex penalties such as the SCAD and MCP, which do not involve the restrictive incoherence conditions from Lasso-based theory. Projected gradient descent methods may be used to obtain these optima in an efficient manner.
Po-Ling Loh is an assistant professor in the statistics department at the Wharton School at the University of Pennsylvania. She received a PhD in statistics from Berkeley in 2014 and a BS in math with a minor in English from Caltech in 2009. Po-Ling is interested in problems in high-dimensional statistics. She is also interested in nonconvex optimization techniques and how they may be used to promote sparsity and increase robustness.
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