# Estimating ensemble flows on a hidden Markov chain

arXiv: https://arxiv.org/abs/1905.09119 · HTML: https://mlsanity.com/paper/1905.09119/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 May 2019.

## Built on by (most cited first, 4 of 4)

- [Proximal Optimal Transport Modeling of Population Dynamics](https://mlsanity.com/paper/2106.06345/) (2021)
- [Estimating Latent Population Flows from Aggregated Data via Inversing Multi-Marginal Optimal Transport](https://mlsanity.com/paper/2212.14527/) (2022)
- [Inference of collective Gaussian hidden Markov models](https://mlsanity.com/paper/2107.11662/) (2021)
- [Imitation-regularized Optimal Transport on Networks: Provable Robustness and Application to Logistics Planning](https://mlsanity.com/paper/2402.17967/) (2024)

## Abstract (arXiv)

We propose a new framework to estimate the evolution of an ensemble of indistinguishable agents on a hidden Markov chain using only aggregate output data. This work can be viewed as an extension of the recent developments in optimal mass transport and Schr"odinger bridges to the finite state space hidden Markov chain setting. The flow of the ensemble is estimated by solving a maximum likelihood problem, which has a convex formulation at the infinite-particle limit, and we develop a fast numerical algorithm for it. We illustrate in two numerical examples how this framework can be used to track the flow of identical and indistinguishable dynamical systems.