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.

在大数据领域中，我们提出两种分布式优化技术，用于解决分布式统计方法和计算的问题；同时，我们还介绍了一种基于Group ADMM算法的分布式坐标下降算法，以获得通信效率高的正则化估计。实验证明了我们提出算法的有效性。

分布式线性回归与组合协变量