Distributional observability of probabilistic Boolean networks

A probabilistic Boolean network (PBN) is a discrete network composed of a family of Boolean networks together with a set of probabilities governing the selection of a Boolean network at each time step. We introduce in this paper a novel observability problem for PBNs. Specifically, we assume that the values of the initial state of the PBN are not known with certainty, but can be described by probability distributions. We ask ourselves under which conditions it is possible to uniquely determine the probability distribution of initial states when giving only knowledge of the evolution of the probability distributions of network outputs. We propose a complete answer to this problem using a linear algebra approach. Several examples, both artificial and real-world, are given and illustrate the viability of the proposed theoretical results. (C) 2021 Elsevier B.V. All rights reserved.