Communication-Efficient Nonparametric Quantile Regression via Random Features

This paper introduces a refined algorithm designed for distributed nonparametric quantile regression in a reproducing kernel Hilbert space (RKHS). Unlike existing nonparametric approaches that primarily address homogeneous data, our approach utilizes kernel-based quantile regression to effectively model heterogeneous data. Moreover, we integrate the concepts of random features (RF) and communication-efficient surrogate likelihood (CSL) to ensure accurate estimation and enhance computational efficiency in distributed settings. Specifically, we employ an embedding technique to map the original data into RF spaces, enabling us to construct an extended surrogate loss function. This function can be locally optimized using an iterative alternating direction method of multipliers (ADMM) algorithm, minimizing the need for extensive computation and communication within the distributed system. The paper thoroughly investigates the asymptotic properties of the distributed estimator and provides convergence rates of the excess risk. These properties are established under mild technical conditions and are comparable to state-of-the-art results in the literature. Additionally, we validate the effectiveness of the proposed algorithm through a comprehensive set of synthetic examples and a real data study, effectively highlighting its advantages and practical utility.