  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.
