Partially-Observed Discrete Dynamical Systems

This paper introduces a new signal model called partially-observed discrete dynamical systems (PODDS). This signal model is a special case of the hidden Markov model (HMM), where the state is a vector containing the information of different components of the system, and each component takes its value from a finite real-valued set. This signal model is currently treated as a finite-state HMM, where maximum a posteriori (MAP) criterion is used for state estimator purpose. This paper takes advantage of the discrete structure of the state variables in PODDS and develops the optimal componentwise MAP (CMAP) state estimator, which yields the MAP solution in each state variable. A fully-recursive process is provided for computation of this optimal estimator, followed by introducing a specific instance of the PODDS model suitable for regulatory networks observed through noisy time series data. The high performance of the proposed estimator is demonstrated by numerical experiments with a PODDS model of random regulatory networks.