Communication-efficient distributed estimation of partially linear additive models for large-scale data

Abstract

Distributed estimation for parametric models has drawn attention in modern statistical learning, but few studies focus on semiparametric models. In this paper, we propose two communication-efficient distributed estimators for partially linear additive models with high-dimensional covariates. The commonly used B-spline basis functions are first applied to approximate the nonparametric functions and then we construct a profiled communication-efficient surrogate loss function with Lasso penalty based on one local machine solving the final optimization problem. Further, to reduce the effect of local machines and improve the stability of the algorithm, a profiled gradient-enhanced loss estimator is derived. The resulting two estimators and their theoretical convergence rates for both parametric and nonparametric components are established. The finite-sample performance of the proposed estimators is studied through simulations and an application to appliances energy prediction data set is also presented.