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 component-wise 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.