Session: Optimization and Statistics at Scale
Chair: Mateo Diaz
Cluster: Optimization For Data Science
Talk 1: A superlinearly convergent subgradient method for sharp semismooth problems
Speaker: Vasilis Charisopoulos
Abstract: Nonsmooth optimization problems appear throughout machine learning and signal processing. However, standard first-order methods for nonsmooth optimization can be slow for "poorly conditioned" problems. In this talk, I will present a locally accelerated first-order method that is less sensitive to conditioning and achieves superlinear (i.e., double-exponential) convergence near solutions for a broad family of problems. The algorithm is inspired by Newton's method for solving nonlinear equations.
Talk 2: Commutator Stepsize Schedule
Speaker: Henry Shugart
Abstract: TBD
Talk 3: The radius of statistical efficiency
Speaker: Mateo Diaz
Abstract: Classical results in asymptotic statistics show that the Fisher information matrix controls the difficulty of estimating a statistical model from observed data. In this work, we introduce a companion measure of robustness of an estimation problem: the radius of statistical efficiency (RSE) is the size of the smallest perturbation to the problem data that renders the Fisher information matrix singular. We compute the RSE up to numerical constants for a variety of test bed problems, including principal component analysis, generalized linear models, phase retrieval, bilinear sensing, and matrix completion. In all cases, the RSE quantifies the compatibility between the covariance of the population data and the latent model parameter. Interestingly, we observe a precise reciprocal relationship between the RSE and the intrinsic complexity/sensitivity of the problem instance, paralleling the classical Eckart–Young theorem in numerical analysis.
