Filtering for Aggregate Hidden Markov Models with Continuous Observations

2020/11/04 by Qinsheng Zhang, Rahul Singh, Zhang, Qinsheng +3
Computer Science · #49Q22 #62F15 #62Mxx #93E11 #Bayesian Methods and Mixture Models #Bayesian Modeling and Causal Inference #FOS: Computer and information sciences #FOS: Electrical engineering #FOS: Mathematics #Information Theory (cs.IT) #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Optimization and Control (math.OC) #Systems and Control (eess.SY) #Target Tracking and Data Fusion in Sensor Networks #electronic engineering #information engineering

paper · pdf · doi:10.48550/arxiv.2011.02521

openalex publication_date 2020/11/04 · openalex created_date 2020/11/09 · openalex updated_date 2026/07/28

Abstract

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.

Related

• Inference of collective Gaussian hidden Markov models
• Learning Hidden Markov Models from Aggregate Observations
• Estimation in Markov Models from Aggregate Data
• An Expectation-Maximization Algorithm for Continuous-time Hidden Markov Models
• Consistently Estimating Markov Chains with Noisy Aggregate Data