Robust Intervention in Probabilistic Boolean Networks

Probabilistic Boolean networks (PBNs) have been recently introduced as a paradigm for modeling genetic regulatory networks. One of the objectives of PBN modeling is to use the network for the design and analysis of intervention strategies aimed at moving the network out of undesirable states, such as those associated with disease, and into desirable ones. To date, a number of intervention strategies have been proposed in the context of PBNs. However, all these techniques assume perfect knowledge of the transition probability matrix of the PBN. Such an assumption cannot be satisfied in practice since the presence of noise and the availability of limited number of samples will prevent the transition probabilities from being accurately determined. Moreover, even if the exact transition probabilities could be estimated from the data, mismatch between the PBN model and the actual genetic regulatory network will invariably be present. Thus, it is important to study the effect of modeling errors on the final outcome of an intervention strategy and one of the goals of this paper is to do precisely that when the uncertainties are in the entries of the transition probability matrix. In addition, the paper develops a robust intervention strategy that is obtained by minimizing the worst-case cost over the uncertainty set.