A fundamental problem of biology is to construct gene regulatory networks that characterize the operational interaction among genes. The term “gene” is used generically because such networks could involve gene products. Numerous inference algorithms have been proposed. The validity, or accuracy, of such algorithms is of central concern. Given data generated by a ground-truth network, how well does a model network inferred from the data match the data-generating network? This chapter discusses a general paradigm for inference validation based on defining a distance between networks and judging validity according to the distance between the original network and the inferred network. Such a distance will typically be based on some network characteristics, such as connectivity, rule structure, or steady-state distribution. It can also be based on some objective for which the model network is being employed, such as deriving an intervention strategy to apply to the original network with the aim of correcting aberrant behavior. Rather than assuming that a single network is inferred, one can take the perspective that the inference procedure leads to an “uncertainty class” of networks, to which belongs the ground-truth network. In this case, we define a measure of uncertainty in terms of the cost that uncertainty imposes on the objective, for which the model network is to be employed, the example discussed in the current chapter involving intervention in the yeast cell cycle network.

Introduction

From a translational perspective, we are interested in gene regulatory networks (GRNs) as a vehicle to derive optimal intervention strategies for regulatory pathologies, cancer being the salient example (see [1–3] for reviews and [4] for extensive coverage). Two basic intervention approaches have been considered for gene regulatory networks in the context of probabilistic Boolean networks (PBNs), external control and structural intervention [4], a key to intervention being that the dynamic behavior of a PBN can be modeled by a Markov chain, thereby making intervention in PBNs amenable to the theory of Markov decision processes. Perhaps we should note that the ability of Markov chains to model GRNs has a long history in translational genomics [5]. External control is based on externally manipulating the value of a control gene to beneficially alter the steady-state distribution, either indirectly via a one-step cost function [6] or directly via an objective function based on the steady-state distribution [7, 8].