Distributed non-convex regularization for generalized linear regression

Distributed penalized generalized linear regression algorithms have been widely studied in recent years. However, they all assume that the data should be randomly distributed. In real applications, this assumption is not necessarily true, since the whole data are often stored in a non-random manner. To tackle this issue, a non- convex penalized distributed pilot sample surrogate negative log-likelihood learning procedure is developed, which can realize distributed high-dimensional variable selection for generalized linear models, and be adaptive to the non-random situations. The established theoretical results and numerical studies all validate the proposed method.