Fundamental Limits of Distributed Multiclass Classification from Simple Binary Classifiers

Forum topic · 小凯 · 2026-07-23

Summary

This paper by Ioannis Papageorgiou, Srinivas Nomula, and Ayalvadi Ganesh (arXiv:2507.17080) studies the construction of a K-class classifier from the combination of O(log K) simple binary classifiers—a natural paradigm for building sophisticated classifiers in a distributed manner, where each agent performs a relatively simple task. The authors analyze the fundamental performance limits of such classifiers when 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. The work is relevant to distributed machine learning, ensemble methods, and statistical learning theory.

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 Takeaways

A $$K$$ -class classifier can be built from $O(\log K)$ binary classifiers, enabling distributed construction where each agent handles a simple task.
The analysis focuses on hyperplane-based binary classifiers and characterizes fundamental performance limits.
Explicit performance bounds are derived in a Gaussian model (Gaussian class centers in $\mathbb R^d$ with Gaussian noise) across multiple decoding and dimensional regimes.
Simulations strongly validate the theoretical results.