Modeling and Estimation of Discrete-Time Reciprocal Processes via Probabilistic Graphical Models
This work addresses the modeling and estimation of reciprocal processes, which are acausal generalizations of Markov processes, for researchers in probabilistic graphical models and signal processing, but it appears incremental as it builds on existing dynamical models.
The paper tackled the problem of modeling discrete-time reciprocal processes by introducing a probabilistic graphical model, which enabled a principled solution to the smoothing problem using message passing algorithms, with convergence analysis revisited via the Hilbert metric for finite state spaces.
Reciprocal processes are acausal generalizations of Markov processes introduced by Bernstein in 1932. In the literature, a significant amount of attention has been focused on developing dynamical models for reciprocal processes. In this paper, we provide a probabilistic graphical model for reciprocal processes. This leads to a principled solution of the smoothing problem via message passing algorithms. For the finite state space case, convergence analysis is revisited via the Hilbert metric.