On the Feasibility of Distributed Kernel Regression for Big Data

TL;DR

This paper investigates the theoretical validity of distributed kernel regression for big data, demonstrating that with proper segmentation, the method achieves consistent generalization performance, supported by simulations and real data.

Contribution

It provides the first theoretical analysis confirming the consistency of distributed kernel regression under big data conditions.

Findings

Distributed kernel regression is generalization consistent with proper segmentation.

Theoretical bounds are established for the generalization error.

Simulation and real data examples support the method's effectiveness.

Abstract

In modern scientific research, massive datasets with huge numbers of observations are frequently encountered. To facilitate the computational process, a divide-and-conquer scheme is often used for the analysis of big data. In such a strategy, a full dataset is first split into several manageable segments; the final output is then averaged from the individual outputs of the segments. Despite its popularity in practice, it remains largely unknown that whether such a distributive strategy provides valid theoretical inferences to the original data. In this paper, we address this fundamental issue for the distributed kernel regression (DKR), where the algorithmic feasibility is measured by the generalization performance of the resulting estimator. To justify DKR, a uniform convergence rate is needed for bounding the generalization error over the individual outputs, which brings new and challenging issues in the big data setup. Under mild conditions, we show that, with a proper number of segments, DKR leads to an estimator that is generalization consistent to the unknown regression function. The obtained results justify the method of DKR and shed light on the feasibility of using other distributed algorithms for processing big data. The promising preference of the method is supported by both simulation and real data examples.