Particle filters for partially-observed Boolean dynamical systems

Abstract

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 propose approximate MMSE filtering and smoothing algorithms based on the auxiliary particle filter (APF) method from sequential Monte-Carlo theory. These algorithms are used jointly with maximum-likelihood (ML) methods for simultaneous state and parameter estimation in POBDS models. In the presence of continuous parameters, ML estimation is performed using the expectation-maximization (EM) algorithm; we develop for this purpose a special smoother which reduces the computational complexity of the EM algorithm. The resulting particle-based adaptive filter is applied to a POBDS model of Boolean gene regulatory networks observed through noisy RNA-Seq time series data, and performance is assessed through a series of numerical experiments using the well-known cell cycle gene regulatory model. (Mahdi Imani), ulisses@ece.tamu.edu (Ulisses Braga-Neto).becomes impractical due to large computational and memory requirements. In [3], an approximate sequential Monte-Carlo (SMC) algorithm was proposed to compute the BKF using sequential importance resampling (SIR). By contrast, we develop here SMC algorithms for both the BKF and fixed-interval BKS based on the more efficient auxiliary particle filter (APF) algorithm [17].The BKF and BKS require for their application that all system parameters be known. In the case where noise intensities, the network topology, or observational parameters are not known or only partially known, an adaptive scheme to simultaneously estimate the state and parameters of the system is required. An exact adaptive filtering framework to accomplish that task was proposed recently in [18], which is based on the BKF and BKS in conjunction with maximum-likelihood estimation of the parameters. In this paper, we develop an accurate and efficient particle filtering implementation of the adaptive filtering framework in [18], which is suitable for large systems.In the case where the parameter space is discrete (finite), the adaptive filter corresponds to a bank of particle filters in parallel, which is reminiscent of the multiple

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