Fundamental Limits of Distributed Multiclass Classification from Simple Binary Classifiers

Forum topic · 小凯 · 2026-07-23

Summary

A paper by Ioannis Papageorgiou, Srinivas Nomula, and Ayalvadi Ganesh (arXiv:2507.17080) studies the fundamental performance limits of constructing a K-class classifier from a combination of O(log K) simple binary classifiers. This paradigm enables building sophisticated classification in a distributed manner, with each agent performing a relatively straightforward task. The authors analyze the case where the binary classifiers are hyperplanes. In a stylized Gaussian setting, where the K class centers are independent Gaussian points in R^d and observations are corrupted by Gaussian noise, they derive explicit performance bounds across several decoding and dimensional regimes. Extensive simulation experiments provide strong empirical validation of the theoretical results.

Paper Overview

Field: Machine Learning
Authors: Ioannis Papageorgiou, Srinivas Nomula, Ayalvadi Ganesh
Published: 2026-07-22
arXiv: 2507.17080

Abstract

We consider the problem of constructing a $$K$$ -class classifier from the combination of $O(\log K)$ simple binary classifiers -- this is a natural paradigm to construct a sophisticated classifier in a distributed manner with each agent performing a relatively straightforward task. We study the fundamental performance limits of such a classifier when the corresponding binary classifiers are hyperplanes. For a stylized Gaussian setting where the $$K$$ class centers are independent Gaussian points in $\mathbb R^d$ and the observations are corrupted by Gaussian noise, we derive explicit performance bounds across several decoding and dimensional regimes. Extensive simulation experiments provide strong empirical validation of the presented theoretical results.

Key Contributions

A framework for building $$K$$ -class classifiers from only $O(\log K)$ binary hyperplane classifiers, suitable for distributed implementations.
Explicit performance bounds in a stylized Gaussian model: class centers drawn as independent Gaussian points in $\mathbb R^d$ , with Gaussian noise corrupting observations.
Analysis covering multiple decoding schemes and dimensional regimes.
Simulation experiments that strongly validate the theoretical results.

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