📝 SummarXiv

Abstract

Dynamical systems in chemistry and biology are complex, and one often does not have comprehensive knowledge about the interactions involved. Chemical reaction network (CRN) inference aims to identify, from observing species concentrations over time, the unknown reactions between the species. Existing approaches largely focus on identifying a single, most likely CRN, without addressing uncertainty about the network structure. However, it is important to quantify structural uncertainty to have confidence in our inference and predictions. In this work, we do so by inferring an approximate posterior distribution over CRN structures. This is done by keeping a large set of suboptimal solutions found through sparse optimisation, in contrast to existing optimisation approaches which discard suboptimal solutions. We find that inducing reaction sparsity with nonconvex penalty functions results in more parsimonious CRNs compared to the popular lasso regularisation. In a real-data example where multiple CRNs have been previously suggested, our method simultaneously recovers reactions proposed from different literature. Our emphasis on network-level probabilities enables a novel, hierarchical representation of structural ambiguities in the space of CRNs. This readily translates into alternative reaction pathways suggested by the available data, thus guiding the efforts of future experimental design.