Incremental inference of collective graphical models

TL;DR

This paper introduces an online algorithm for estimating aggregate marginals of Markov chains from noisy data, using a novel sliding window Sinkhorn belief propagation method for collective dynamics inference.

Contribution

It presents a new incremental inference algorithm combining belief propagation and optimal transport for aggregate data, enabling real-time collective dynamics analysis.

Findings

Effective in inferring population flow from aggregate data

Utilizes a sliding window approach for online inference

Builds upon multi-marginal optimal transport and Sinkhorn algorithms

Abstract

We consider incremental inference problems from aggregate data for collective dynamics. In particular, we address the problem of estimating the aggregate marginals of a Markov chain from noisy aggregate observations in an incremental (online) fashion. We propose a sliding window Sinkhorn belief propagation (SW-SBP) algorithm that utilizes a sliding window filter of the most recent noisy aggregate observations along with encoded information from discarded observations. Our algorithm is built upon the recently proposed multi-marginal optimal transport based SBP algorithm that leverages standard belief propagation and Sinkhorn algorithm to solve inference problems from aggregate data. We demonstrate the performance of our algorithm on applications such as inferring population flow from aggregate observations.