On the Inversion‐Free Newton's Method and Its Applications

Abstract

SummaryIn this paper, we survey the recent development of inversion‐free Newton's method, which directly avoids computing the inversion of Hessian, and demonstrate its applications in estimating parameters of models such as linear and logistic regression. A detailed review of existing methodology is provided, along with comparisons of various competing algorithms. We provide numerical examples that highlight some deficiencies of existing approaches, and demonstrate how the inversion‐free methods can improve performance. Motivated by recent works in literature, we provide a unified subsampling framework that can be combined with the inversion‐free Newton's method to estimate model parameters including those of linear and logistic regression. Numerical examples are provided for illustration.