Estimating Latent Population Flows from Aggregated Data via Inversing Multi-Marginal Optimal Transport

TL;DR

This paper introduces a novel approach using multi-marginal optimal transport to estimate dynamic population flows from aggregated data, overcoming limitations of traditional Markov models affected by uncertainties.

Contribution

It proposes a new MOT-based framework that learns cost functions to model time-varying transition patterns from aggregated data, improving estimation accuracy.

Findings

Outperforms existing methods in real-world population flow estimation

Effectively captures time-dependent transition dynamics

Demonstrates robustness to uncertainties like traffic and weather

Abstract

We study the problem of estimating latent population flows from aggregated count data. This problem arises when individual trajectories are not available due to privacy issues or measurement fidelity. Instead, the aggregated observations are measured over discrete-time points, for estimating the population flows among states. Most related studies tackle the problems by learning the transition parameters of a time-homogeneous Markov process. Nonetheless, most real-world population flows can be influenced by various uncertainties such as traffic jam and weather conditions. Thus, in many cases, a time-homogeneous Markov model is a poor approximation of the much more complex population flows. To circumvent this difficulty, we resort to a multi-marginal optimal transport (MOT) formulation that can naturally represent aggregated observations with constrained marginals, and encode time-dependent transition matrices by the cost functions. In particular, we propose to estimate the transition flows from aggregated data by learning the cost functions of the MOT framework, which enables us to capture time-varying dynamic patterns. The experiments demonstrate the improved accuracy of the proposed algorithms than the related methods in estimating several real-world transition flows.