Distributed Linear Regression with Compositional Covariates
Yue Chao Lei Huang Xuejun Ma
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.