Cellular Tree Classifiers

TL;DR

This paper introduces cellular tree classifiers that enable consistent distributed classification by splitting data across multiple cells, addressing a key challenge in parallel computing environments.

Contribution

It demonstrates the existence of two consistent classifiers within the cellular tree framework for nonatomic distributions, advancing distributed classification theory.

Findings

Two different consistent classifiers are constructed.

Consistency holds for nonatomic distributions.

Framework supports parallel and distributed data processing.

Abstract

The cellular tree classifier model addresses a fundamental problem in the design of classifiers for a parallel or distributed computing world: Given a data set, is it sufficient to apply a majority rule for classification, or shall one split the data into two or more parts and send each part to a potentially different computer (or cell) for further processing? At first sight, it seems impossible to define with this paradigm a consistent classifier as no cell knows the "original data size", $n$. However, we show that this is not so by exhibiting two different consistent classifiers. The consistency is universal but is only shown for distributions with nonatomic marginals.