Least-Square Approximation for a Distributed System

In this work, we develop a distributed least squares approximation (DLSA) method that is able to solve large family of regression problems (e.g., linear regression, logistic and Cox's model) on system. By approximating the local objective function using quadratic form, are obtain combined estimator by taking weighted average estimators. The resulting proved be statistically as efficient global estimator. Moreover, it requires only one round communication. We further conduct shrinkage estimation based DLSA an adaptive Lasso approach. solution can easily obtained LARS algorithm master node. It theoretically shown possesses oracle property selection consistent newly designed Bayesian information criterion (DBIC). finite sample performance computational efficiency illustrated extensive numerical study airline dataset. dataset 52 GB in size. entire methodology has been implemented Python for {\it de-facto} standard Spark proposed system takes 26 minutes estimator, which more memory friendly than conventional methods.