Design of probabilistic Boolean networks under the requirement of contextual data consistency

A key issue of genomic signal processing is the design of gene regulatory networks. A probabilistic Boolean network (PBN) is composed of a family of Boolean networks. It stochastically switches between its constituent networks (contexts). For network design, connectivity and transition rules must be inferred from data via some optimization criterion. Except rarely, the optimal rule for a gene will not be a perfect predictor because there will be inconsistencies in the data. It would be natural to model these inconsistencies to reflect changes in PBN contexts. If we assume inconsistencies result from the data arising from a random function, then design involves finding the realizations of a random function and the probability mass on those realizations so that the resulting random function best fits the data relative to the expectation of its output and does so using a minimal number of realizations. We propose PBN design satisfying the biological assumption that data are consistent within a context, for which the distribution of the network agrees with the empirical distribution of the data, and such that this is accomplished with a minimal number of contexts. The design also satisfies the biological constraint that, because the network spends the great majority of time in its attractors, all data states should be attractor states in the model