Kernel-Based Particle Filtering for Scalable Inference in Partially Observed Boolean Dynamical Systems

Abstract

This paper addresses the inference challenges associated with a class of hidden Markov models with binary state variables, known as partially observed Boolean dynamical systems (POBDS). POBDS have demonstrated remarkable success in modeling the ON and OFF dynamics of genes, microbes, and bacteria in systems biology, as well as in network security to represent the propagation of attacks among interconnected elements. Despite existing optimal and approximate inference solutions for POBDS, scalability remains a significant issue due to the computational cost associated with likelihood evaluations and the exploration of extensive parameter spaces. To overcome these challenges, this paper proposes a kernel-based particle filtering approach for large-scale inference of POBDS. Our method employs a Gaussian process (GP) to efficiently represent the expensive-to-evaluate likelihood function across the parameter space. The likelihood evaluation is approximated using a particle filtering technique, enabling the GP to account for various sources of uncertainty, including limited likelihood evaluations. Leveraging the GP's predictive behavior, a Bayesian optimization strategy is derived for effectively seeking parameters yielding the highest likelihood, minimizing the overall computational burden while balancing exploration and exploitation. The proposed method's performance is demonstrated using two biological networks: the mammalian cell-cycle network and the T-cell large granular lymphocyte leukemia network.

Keywords: Bayesian Optimization; Biological Networks; Inference; Partially-Observed Boolean Dynamical Systems; Particle Filters.

Fig. 1.

Mammalian Cell-Cycle network pathway diagram.

Fig. 2.

Performance comparison of our method and simulated annealing throughout topology optimization of the mammalian cell-cycle network: (a) average log-likelihood progress (b) average connectivity error progress (c) average state estimation MSE progress.

Fig. 3.

Changes of connectivity error in the presence of different process noise ($p$) in the cell-cycle network.

Fig. 4.

T-LGL leukemia network pathway diagram

Fig. 5.

Performance comparison of our method and simulated annealing throughout topology optimization of the T-LGL leukemia network: (a) average log-likelihood progress (b) average connectivity error progress (c) average state estimation MSE progress.