Abstract

In this talk I will present a generalized Newton homotopy (GNH) algorithm for subset selection in high-dimensional regression. This algorithm is designed to compute the solution path of the KKT equations for the L0 penalized least squares problem, which is another formulation of subset selection.  Under certain regularity conditions, GNH converges globally and attains the oracle estimator in finite steps with high probability. For data with large sample sizes or when data is stored in distributed databases, we also consider a distributed implementation of GNH. We show that the distributed GNH still attains the oracle estimator in a controllable number of rounds of communications.