Bayesian Optimization for State and Parameter Estimation of Dynamic Networks with Binary Space

This paper focuses on joint state and parameter estimation in partially observed Boolean dynamical systems (POBDS), a hidden Markov model tailored for modeling complex networks with binary state variables. The majority of current techniques for parameter estimation rely on computationally expensive gradient-based methods, which become intractable in most practical applications with large size of networks. We propose a gradient-free approach that uses Gaussian processes to model the expensive log-likelihood function and utilizes Bayesian optimization for efficient likelihood search over parameter space. Joint state estimation is also achieved alongside parameter estimation using the Boolean Kalman filter. The performance of the proposed method is demonstrated using gene regulatory networks observed through synthetic gene-expression data. The numerical results demonstrate the scalability and effectiveness of the proposed method in the joint estimation of the model parameters and genes' states.