Communication-efficient distributed statistical learning

We present the Communication-efficient Surrogate Likelihood (CSL) framework for solving distributed statistical learning problems. CSL provides a communication-efficient surrogate to the global likelihood that can be used for low-dimensional estimation, high-dimensional regularized estimation and Bayesian inference. For low-dimensional estimation, CSL provably improves upon the averaging schemes and facilitates the construction of confidence intervals. For high-dimensional regularized estimation, CSL leads to a minimax optimal estimator with minimal communication cost. For Bayesian inference, CSL can be used to form a communication-efficient quasi-posterior distribution that converges to the true posterior. This quasi-posterior procedure significantly improves the computational efficiency of MCMC algorithms even in a non-distributed setting. The methods are illustrated through empirical studies.