Robust regression for non-randomly distributed big data with application to nonconvex penalized learning

Abstract

Distributed statistical learning for massive data has attracted enormous attention recently.There are two noteworthy issues in the existing methods. First, they all require that the massive data are randomly distributed on different machines, which is seldom the case in practice. Second, they are usually built upon the least squares, which are sensitive to the heavy-tailed noise and outliers.To fix these problems, we propose a new robust distributed modal regression and also apply it to nonconvex penalized learning problems.The new method can overcome the non-randomly distributed nature of the big data, and the theoretical results also guarantee this statement. Simulation studies and the real world data evaluation are also used to illustrate the proposed methods.