Semi-profiled distributed estimation for high-dimensional partially linear model

Abstract

As a leading example in the semiparametric model, the partially linear model is prominent in modeling complex data. The challenges associated with designing an efficient estimation algorithm in the distributed environment are not yet well addressed. The existing works require a constraint on the number of local machines to guarantee the optimality of the global estimator. In addition, a multi-round profiled estimator will lead to huge communication complexity. To further reduce communication costs, a novel semi-profiled estimation procedure is proposed, which provides an iterative skeleton to reduce estimation error. A new multi-round distributed algorithm based on the centralized semi-profiled estimator is developed, which can estimate the parametric and nonparametric simultaneously. The theoretical results indicate that the corresponding convergence rates can achieve the optimal orders within a constant number of communication rounds. The advantages of the proposed estimation method are demonstrated via numerical experiments on synthetic and real data.