Bayesian topology inference of regulatory networks under partial observability

Biological systems, such as microbial communities in metagenomics and gene regulatory networks (GRNs) in genomics, are composed of a vast number of interacting components observed through inherently noisy data. These systems play a critical role in understanding fundamental biological processes, including gene regulation, microbial interactions, and cellular dynamics. For example, microbial communities involve complex interactions between microbes, bacteria, genes, and small molecules observed through omics data, while GRNs consist of numerous interacting genes observed via various gene-expression technologies. However, reconstructing the topology of such networks poses significant challenges due to their large scale, high dimensionality, and the presence of noise. Existing inference techniques often struggle with scalability, interpretability, and overfitting, making them unsuitable for analyzing large and complex biological systems. To overcome these challenges, this paper proposes a Bayesian topology optimization framework for efficient and scalable inference of regulatory networks modeled as partially-observed Boolean dynamical systems (POBDS). The method combines the Boolean Kalman Filter (BKF) as an optimal estimator for POBDS, with Bayesian optimization, which employs Gaussian Process regression and a topology-inspired kernel function to model the log-likelihood function. Numerical experiments demonstrate the superior performance of our framework. In the p53-MDM2 network, our method accurately infers topology with 8 and 16 unknown regulations, achieving higher log-likelihood with 100 and 200 evaluations, respectively. For the mammalian cell cycle network with 10 unknown regulations, proposed method identifies the correct topology among 59,049 possibilities with lower error and faster convergence.