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.
- Pub Date:
- July 2021
- Statistics - Machine Learning;
- Computer Science - Machine Learning;
- Electrical Engineering and Systems Science - Signal Processing;
- Electrical Engineering and Systems Science - Systems and Control