On the Feasibility of Distributed Kernel Regression for Big Data

by   Yongquan Zhang, et al.

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.


page 1

page 2

page 3

page 4


Learning Theory of Distributed Regression with Bias Corrected Regularization Kernel Network

Distributed learning is an effective way to analyze big data. In distrib...

Distributed Feature Screening via Componentwise Debiasing

Feature screening is a powerful tool in the analysis of high dimensional...

Big Data: the End of the Scientific Method?

We argue that the boldest claims of Big Data are in need of revision and...

A Panel Quantile Approach to Attrition Bias in Big Data: Evidence from a Randomized Experiment

This paper introduces a quantile regression estimator for panel data mod...

On the selection of optimal subdata for big data regression based on leverage scores

Regression can be really difficult in case of big datasets, since we hav...

fplyr: the split-apply-combine strategy for big data in R

We present fplyr, a new package for the R language to deal with big file...

Markov subsampling based Huber Criterion

Subsampling is an important technique to tackle the computational challe...

Please sign up or login with your details

Forgot password? Click here to reset