State Estimation of Stochastic Boolean Networks Based on Event-Triggered Sampling

A stochastic Boolean network (SBN) emerges as a more realistic model for gene regulatory networks than a deterministic Boolean network (BN). In order to reduce output sampling while ensuring a given estimation accuracy, this article proposes an event-triggered sampling strategy for the state estimation of SBNs. Under this strategy, the output is sampled when the one-step prediction mean error exceeds a prespecified threshold. An iterative algorithm for the state probability distribution is proposed based on the algebraic form of SBNs, which determines the optimal state estimation. A matrix inequality method is proposed to calculate the worst-case mean estimation error based on its monotonicity with time. Then, the range of sampling triggering thresholds that minimize the worst-case mean estimation error is obtained. This article demonstrates that the event-triggered sampling strategy can make a tradeoff between estimation error and sampling rate. It explains that the full sampling estimator is a special event-triggered sampling estimator. Finally, the proposed method is applied to BN models of the lac operon in Escherichia coli to analyze the relationship among the sampling triggering threshold, the sampling rate, and the estimation error.