Title: A Stochastic Large-scale Machine Learning Algorithm for Distributed Features and Observations,
Abstract: As the size of modern data sets exceeds the disk and memory capacities of a
single computer, machine learning practitioners have resorted to parallel and
distributed computing. Given that optimization is one of the pillars of machine
learning and predictive modeling, distributed optimization methods have
recently garnered ample attention, in particular when either observations or
features are distributed, but not both. We propose a general stochastic
algorithm where observations, features, and gradient components can be sampled
in a double distributed setting, i.e., with both features and observations
distributed. Very technical analyses establish convergence properties of the
algorithm under different conditions on the learning rate (diminishing to zero
or constant). Computational experiments in Spark demonstrate a superior
performance of our algorithm versus a benchmark in early iterations of the
algorithm, which is due to the stochastic components of the algorithm.