Inference of collective Gaussian hidden Markov models
This work addresses inference challenges in aggregated data analysis for populations, representing an incremental advancement by extending existing methods to Gaussian densities.
The authors tackled the problem of inferring collective Gaussian hidden Markov models from aggregated data generated by many individuals, proposing a collective Gaussian forward-backward algorithm that extends Sinkhorn belief propagation and reduces to the Kalman filter for single individuals, with demonstrated efficacy in experiments.
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.