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Classification with a Network of Partially Informative Agents: Enabling Wise Crowds from Individually Myopic Classifiers

Tong Yao, Shreyas Sundaram

TL;DR

This work tackles online distributed classification with a network of heterogeneous, partially informative agents, each observing local data and restricted to a subset of classes. It introduces a two-tier learning approach: a local posterior update that reweights each agent’s beliefs using its classifier output, and a global min-rule that fuses these beliefs across neighbors to eliminate false classes, enabling asymptotic identification of the true class $\theta^*$ for all agents. The authors prove that, under global identifiability and positive initial beliefs, false classes are rejected exponentially fast and $\mu_{i,t}(\theta^*) \to 1$ almost surely, with a convergence rate independent of network size and enhanced by including support agents. Empirical validation on CIFAR-10 with random forests and MobileNet demonstrates faster, robust learning compared to averaging or max-aggregation, illustrating the practical potential of wise crowds built from locally myopic classifiers.

Abstract

We consider the problem of classification with a (peer-to-peer) network of heterogeneous and partially informative agents, each receiving local data generated by an underlying true class, and equipped with a classifier that can only distinguish between a subset of the entire set of classes. We propose an iterative algorithm that uses the posterior probabilities of the local classifier and recursively updates each agent's local belief on all the possible classes, based on its local signals and belief information from its neighbors. We then adopt a novel distributed min-rule to update each agent's global belief and enable learning of the true class for all agents. We show that under certain assumptions, the beliefs on the true class converge to one asymptotically almost surely. We provide the asymptotic convergence rate, and demonstrate the performance of our algorithm through simulation with image data and experimented with random forest classifiers and MobileNet.

Classification with a Network of Partially Informative Agents: Enabling Wise Crowds from Individually Myopic Classifiers

TL;DR

This work tackles online distributed classification with a network of heterogeneous, partially informative agents, each observing local data and restricted to a subset of classes. It introduces a two-tier learning approach: a local posterior update that reweights each agent’s beliefs using its classifier output, and a global min-rule that fuses these beliefs across neighbors to eliminate false classes, enabling asymptotic identification of the true class for all agents. The authors prove that, under global identifiability and positive initial beliefs, false classes are rejected exponentially fast and almost surely, with a convergence rate independent of network size and enhanced by including support agents. Empirical validation on CIFAR-10 with random forests and MobileNet demonstrates faster, robust learning compared to averaging or max-aggregation, illustrating the practical potential of wise crowds built from locally myopic classifiers.

Abstract

We consider the problem of classification with a (peer-to-peer) network of heterogeneous and partially informative agents, each receiving local data generated by an underlying true class, and equipped with a classifier that can only distinguish between a subset of the entire set of classes. We propose an iterative algorithm that uses the posterior probabilities of the local classifier and recursively updates each agent's local belief on all the possible classes, based on its local signals and belief information from its neighbors. We then adopt a novel distributed min-rule to update each agent's global belief and enable learning of the true class for all agents. We show that under certain assumptions, the beliefs on the true class converge to one asymptotically almost surely. We provide the asymptotic convergence rate, and demonstrate the performance of our algorithm through simulation with image data and experimented with random forest classifiers and MobileNet.
Paper Structure (15 sections, 9 theorems, 46 equations, 15 figures, 1 algorithm)

This paper contains 15 sections, 9 theorems, 46 equations, 15 figures, 1 algorithm.

Table of Contents

  1. INTRODUCTION
  2. PROBLEM FORMULATION
  3. Observation and Agent Model
  4. Quality of Classifiers
  5. Proposed Learning Rules
  6. Local Update of Posterior
  7. Global Update
  8. Analysis of Convergence
  9. Experiment and Simulation
  10. Dataset and Agent Network
  11. Local Update
  12. Distributed Setting
  13. Improvements in Learning Rate
  14. Conclusions and Future Work
  15. Images

Key Result

Theorem 4.2

Consider any $\theta \in \Theta \setminus \{\theta^*\}$, and an agent $i \in \mathcal{S}(\theta^*,\theta)$. Suppose Assumptions aspt: global ident and aspt: pos init are satisfied, then, the update rules eqn: local update pi hateqn: max filleqn: local update ensure that (i) $\pi_{i,t}(\theta) \to 0$

Figures (15)

  • Figure 1: Demonstration of one time step of the proposed multi-agent classification algorithm.
  • Figure 2: Agent communication topology and their distinguishable classes $\Theta_i$.
  • Figure 3: Local averaging
  • Figure 4: Proposed local update
  • Figure 5: Local beliefs of agent 1.
  • ...and 10 more figures

Theorems & Definitions (19)

  • Definition 2.1
  • Definition 2.2
  • Definition 2.3
  • Definition 2.6
  • Definition 2.7
  • Theorem 4.2
  • Lemma 4.3
  • Theorem 4.4
  • Theorem 4.5
  • Lemma A.1
  • ...and 9 more