Bridging the theory and practice: A unified statistical and optimization perspective

Abstract

Despite many exciting empirical successes in data science, there are significant gaps between theory and inspired-by-theory practices. For example, the standard lasso (\ell_1-penalized least squares regression) is not appropriate for variable selection in non-linear statistical models; uniformly random sampling suggested by theory is not adopted in practical compressive medical imaging; the standard bounded gradient/curvature condition in convex optimization just does not hold in some crucial applications. In this talk, I will present how we addressed these gaps—rigorously—via identifying more general conditions on the problem settings, or even developing completely new theoretical frameworks.