OPTIMAL COMPUTATIONAL AND STATISTICAL RATES OF CONVERGENCE FOR SPARSE NONCONVEX LEARNING PROBLEMS.

ABSTRACT: We provide theoretical analysis of the statistical and computational properties of penalized M-estimators that can be formulated as the solution to a possibly nonconvex optimization problem. Many important estimators fall in this category, including least squares regression with nonconvex regularization, generalized linear models with nonconvex regularization and sparse elliptical random design regression. For these problems, it is intractable to calculate the global solution due to the nonconvex formulation. In this paper, we propose an approximate regularization path-following method for solving a variety of learning problems with nonconvex objective functions. Under a unified analytic framework, we simultaneously provide explicit statistical and computational rates of convergence

SUBMITTER: Wang Z 

PROVIDER: S-EPMC4276088 | biostudies-literature | 2014

REPOSITORIES: biostudies-literature