Particle filters for partially-observed Boolean dynamical systems

Partially-observed Boolean dynamical systems (POBDS) are a general class of nonlinear models with application in estimation and control of Boolean processes based on noisy and incomplete measurements. The optimal minimum mean square error (MMSE) algorithms for POBDS state estimation, namely, the Boolean Kalman filter (BKF) and Boolean Kalman smoother (BKS), are intractable in the case of large systems, due to computational and memory requirements. To address this, we introduce approximate MMSE filtering and smoothing algorithms based on the auxiliary particle filter (APF) method, which are called APF-BKF and APF-BKS, respectively. For joint state and parameter estimation, the APF-BKF is used jointly with maximum-likelihood (ML) methods for simultaneous state and parameter estimation in POBDS models. In the case the unknown parameters are discrete, the proposed ML adaptive filter consists of multiple APF-BKFs running in parallel, in a manner reminiscent of the Multiple Model Adaptive Estimation (MMAE) method in classical linear filtering theory. In the presence of continuous parameters, the proposed ML adaptive filter is based on an efficient particle-based expectation maximization (EM) algorithm for the POBDS model, which is based on a modified Forward Filter Backward Simulation (FFBSi) in combination with the APF-BKS. The performance of the proposed particle-based adaptive filters is assessed through numerical experiments using a POBDS model of the well-known cell cycle gene regulatory network observed through noisy RNA-Seq time series data. (C) 2017 Elsevier Ltd. All rights reserved.