# Inference of collective Gaussian hidden Markov models

arXiv: https://arxiv.org/abs/2107.11662 · HTML: https://mlsanity.com/paper/2107.11662/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 18 references that are in the map.
- First posted on arXiv 24 Jul 2021.

## Builds on (most cited first, 6 of 6)

- [Inference with Aggregate Data: An Optimal Transport Approach](https://mlsanity.com/paper/2003.13933/) (2020)
- [Estimating ensemble flows on a hidden Markov chain](https://mlsanity.com/paper/1905.09119/) (2019)
- [Bethe Projections for Non-Local Inference](https://mlsanity.com/paper/1503.01397/) (2015)
- [Feedback Particle Filter for Collective Inference](https://mlsanity.com/paper/2010.06655/) (2020)
- [Incremental inference of collective graphical models](https://mlsanity.com/paper/2006.15035/) (2020)
- [Filtering for Aggregate Hidden Markov Models with Continuous Observations](https://mlsanity.com/paper/2011.02521/) (2020)

## Abstract (arXiv)

We consider inference problems for a class of continuous state collective hidden Markov models, where the data is recorded in aggregate (collective) form generated by a large population of individuals following the same dynamics. We propose an aggregate inference algorithm called collective Gaussian forward-backward algorithm, extending recently proposed Sinkhorn belief propagation algorithm to models characterized by Gaussian densities. Our algorithm enjoys convergence guarantee. In addition, it reduces to the standard Kalman filter when the observations are generated by a single individual. The efficacy of the proposed algorithm is demonstrated through multiple experiments.