Fundamental limits of distributed multiclass classification from simple binary decisions

2026-07-21

AI Summary

This work investigates the efficient construction of multiclass classifiers from a small number of simple binary classifiers and characterizes their fundamental performance limits in distributed settings. By composing $O(\log K)$ hyperplane-based binary classifiers to achieve $K$-class classification, the study establishes, for the first time under Gaussian data and noise assumptions, rigorous theoretical bounds on the achievable performance of this paradigm. Leveraging tools from information theory, statistical learning theory, and high-dimensional geometry, the paper derives explicit error bounds that depend on data dimensionality and decoding strategies. These theoretical results are corroborated through simulations, which confirm the tightness of the bounds and reveal the optimal performance frontier attainable by such ensembles of combined binary classifiers.

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.

Problem

• distributed classification
• multiclass classification
• binary classifiers
• fundamental limits
• hyperplane

Innovation

• distributed classification
• binary classifiers
• fundamental limits
• Gaussian mixture model
• hyperplane decision boundaries