Distributed Learning of Distributions via Social Sampling

TL;DR

This paper introduces a social sampling-based protocol for distributed estimation of discrete distributions, demonstrating convergence and the influence of network topology through theoretical analysis and simulations.

Contribution

It proposes a novel message-passing protocol for distributed distribution learning inspired by social networks, with proven convergence properties.

Findings

Protocol converges almost surely.

Different consensus regimes are identified.

Network topology affects convergence behavior.

Abstract

A protocol for distributed estimation of discrete distributions is proposed. Each agent begins with a single sample from the distribution, and the goal is to learn the empirical distribution of the samples. The protocol is based on a simple message-passing model motivated by communication in social networks. Agents sample a message randomly from their current estimates of the distribution, resulting in a protocol with quantized messages. Using tools from stochastic approximation, the algorithm is shown to converge almost surely. Examples illustrate three regimes with different consensus phenomena. Simulations demonstrate this convergence and give some insight into the effect of network topology.