Title: 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.