Optimizing Consistency-Based Design of Context-Sensitive Gene Regulatory Networks

When designing a gene regulatory network, except in rare circumstances there will be inconsistencies in the data. Modeling data inconsistencies fits naturally into the framework of probabilistic Boolean networks (PBNs). This model consists of a family of deterministic models and the overall model is based on random switching between constituent networks, each of which determines a context. A previous paper has proposed an inference procedure for PBNs to achieve data consistency within constituent networks. This paper proposes optimization methods targeted at two data-consistent design issues having to do with network structure: (1) generalization (namely, model selection) arising from the one-to-many mapping between the data set and PBN model; (2) model reduction under constraint on network connectivity, which is typically made for computational, statistical, or biological reasons. Regarding generalization, we combine connectivity and minimal logical realization to formulate the optimality criterion and propose two algorithms to solve it, the second algorithm guaranteeing a minimally connected PBN. Regarding constrained connectivity, we rephrase it as a lossy coding problem and develop an algorithm to find a best subset of predictors from the full set of predictors with the objective of minimizing probability of prediction error