Distributed Learning with Dependent Samples

TL;DR

This paper extends the analysis of distributed kernel ridge regression to dependent data sequences, deriving optimal learning rates and conditions for non-i.i.d. samples using integral operator methods.

Contribution

It introduces a novel integral operator approach to analyze learning rates for dependent data in distributed kernel ridge regression, expanding applicability beyond i.i.d. samples.

Findings

Derived optimal learning rates for dependent sequences

Established sufficient conditions for mixing properties to ensure optimal rates

Extended distributed learning theory to non-i.i.d. data

Abstract

This paper focuses on learning rate analysis of distributed kernel ridge regression for strong mixing sequences. Using a recently developed integral operator approach and a classical covariance inequality for Banach-valued strong mixing sequences, we succeed in deriving optimal learning rate for distributed kernel ridge regression. As a byproduct, we also deduce a sufficient condition for the mixing property to guarantee the optimal learning rates for kernel ridge regression. Our results extend the applicable range of distributed learning from i.i.d. samples to non-i.i.d. sequences.