Yue Chao

Massive datasets pose a serious challenge to traditional statistical methods. Modal regression has greater robustness and high inference efficiency compared to mean regression and likelihood-based methods. In this article, we present a robust distributed least squares approximation (RDLSA) method for heterogeneously distributed massive datasets under the modal regression framework. Specifically, we first approximate the local objective function for each worker/server/machine by using the Taylor expansion, where it is necessary to remain the main quadratic term. Then, each of local machines calculates their corresponding estimates and uploads them to a master machine for obtaining the approximated aggregated estimator. This process yields a one-step global estimator such that one round of communication is required. Correspondingly, the consistency and asymptotic normality of the estimator are rigorously established under some mild conditions. To further reduce the estimation bias, we perform one Newton-Raphson iteration to obtain a two-step global aggregated estimator. In addition, we develop a variable selection procedure for the distributed modal regression under the robust least squares approximation procedure. Finally, we provide simulation experiments and a real data application to verify the superiority of our method.

1. In time series analysis, a fundamental problem is to explore the serial dependence. The autocorrelation function (ACF) plays a central role in the univariate time series, which can describe the ...

With the availability of extraordinarily huge data sets, solving the problems of distributed statistical methodology and computing for such data sets has become increasingly crucial in the big data area. In this paper, we focus on the distributed sparse penalized linear log-contrast model in massive compositional data. In particular, two distributed optimization techniques under centralized and decentralized topologies are proposed for solving the two different constrained convex optimization problems. Both two proposed algorithms are based on the frameworks of Alternating Direction Method of Multipliers (ADMM) and Coordinate Descent Method of Multipliers(CDMM, Lin et al., 2014, Biometrika). It is worth emphasizing that, in the decentralized topology, we introduce a distributed coordinate-wise descent algorithm based on Group ADMM(GADMM, Elgabli et al., 2020, Journal of Machine Learning Research) for obtaining a communication-efficient regularized estimation. Correspondingly, the convergence theories of the proposed algorithms are rigorously established under some regularity conditions. Numerical experiments on both synthetic and real data are conducted to evaluate our proposed algorithms.