A General Framework for Distributed Inference with Uncertain Models

TL;DR

This paper introduces a unified framework for distributed classification that accounts for uncertainty in agents' likelihood models, enabling consensus in heterogeneous networks with limited data.

Contribution

It extends non-Bayesian social learning to uncertain and non-parametric models, ensuring convergence to centralized results despite model uncertainties.

Findings

Beliefs converge to the same result as centralized methods.

Incorporates uncertainty in likelihood models for practical applications.

Extends framework to non-parametric models.

Abstract

This paper studies the problem of distributed classification with a network of heterogeneous agents. The agents seek to jointly identify the underlying target class that best describes a sequence of observations. The problem is first abstracted to a hypothesis-testing framework, where we assume that the agents seek to agree on the hypothesis (target class) that best matches the distribution of observations. Non-Bayesian social learning theory provides a framework that solves this problem in an efficient manner by allowing the agents to sequentially communicate and update their beliefs for each hypothesis over the network. Most existing approaches assume that agents have access to exact statistical models for each hypothesis. However, in many practical applications, agents learn the likelihood models based on limited data, which induces uncertainty in the likelihood function parameters. In this work, we build upon the concept of uncertain models to incorporate the agents' uncertainty in the likelihoods by identifying a broad set of parametric distribution that allows the agents' beliefs to converge to the same result as a centralized approach. Furthermore, we empirically explore extensions to non-parametric models to provide a generalized framework of uncertain models in non-Bayesian social learning.