Penalized empirical likelihood over decentralized networks

Abstract Empirical likelihood encounters serious computational challenges when applied to massive datasets or multiple data sources distributed across decentralized networks. This paper proposes a constrained empirical likelihood framework for decentralized networks, utilizing a novel penalization technique to obtain a penalized empirical log-likelihood. The resulting empirical log-likelihood ratio statistic is proved to be asymptotically standard chi-squared even for a divergent machine number. However, the optimization problem with the fused penalty is still hard to solve in the decentralized distributed network due to the coupling structure. To address the problem, two novel algorithms are developed to solve the optimization problem in a decentralized manner, with established convergence properties and linear convergence for the second algorithm in specific network structures. The methods are validated through simulations and real data analyses of census income and Ford gobike datasets.