Filtering for Aggregate Hidden Markov Models with Continuous Observations
This work addresses filtering challenges in population-level modeling for domains like epidemiology or sensor networks, but it is incremental as it extends an existing algorithm to continuous observations.
The paper tackles the problem of aggregate inference for large populations modeled by hidden Markov models with continuous observations, proposing a continuous observation collective forward-backward algorithm that extends prior discrete methods, with efficacy demonstrated through numerical experiments.
We consider a class of filtering problems for large populations where each individual is modeled by the same hidden Markov model (HMM). In this paper, we focus on aggregate inference problems in HMMs with discrete state space and continuous observation space. The continuous observations are aggregated in a way such that the individuals are indistinguishable from measurements. We propose an aggregate inference algorithm called continuous observation collective forward-backward algorithm. It extends the recently proposed collective forward-backward algorithm for aggregate inference in HMMs with discrete observations to the case of continuous observations. The efficacy of this algorithm is illustrated through several numerical experiments.