Distributed online quantile regression over networks with quantized communication.

Highlights • We propose the QCdOQR and the l1-QCdOQR algorithms for linear quantile regression problem. • We theoretically study the convergence analyses of the proposed algorithms. • We develop a rule for adaptively adjusting the sparse regularization parameter. Abstract We consider the linear quantile regression problem over networks in this paper. Applying the existing centralized linear quantile regression algorithms to such a problem may encounter some issues, such as the heavy communication burden, the vulnerability to node and/or link failures, and the privacy issues. In a previous work, we proposed a distributed quantile regression algorithm for solving this problem. It is a batch algorithm. However, in practice, each node usually collects data sequentially. To ensure real-time processing, an online manner is preferred. In addition, not only the communication resources of nodes but also the bandwidths of the channels are limited in many real applications over networks. Thus, in these scenarios, only quantized information is allowed for transmission in the channels. In this paper, we propose a quantized communication based distributed online quantile regression (QCdOQR) algorithm. Besides, many natural and artificial systems and signals possess sparsity. We also propose a l 1 -quantized communication based distributed online quantile regression (l 1 -QCdOQR) algorithm to achieve better performance on sparse models. The convergence analyses of the proposed algorithms are studied, and their effectiveness and superiorities are also verified by numerical simulations. [ABSTRACT FROM AUTHOR]