Tractable Learning and Inference for Large-Scale Probabilistic Boolean Networks

Probabilistic Boolean networks (PBNs) have previously been proposed so as to gain insights into complex dynamical systems. However, identification of large networks and their underlying discrete Markov chain which describes their temporal evolution still remains a challenge. In this paper, we introduce an equivalent representation for PBNs, the stochastic conjunctive normal form network (SCNFN), which enables a scalable learning algorithm and helps predict long-run dynamic behavior of large-scale systems. State-of-the-art methods turn out to be 400 times slower for middle-sized networks (i.e., containing 100 nodes) and incapable of terminating for large networks (i.e., containing 1000 nodes) compared to the SCNFN-based learning, when attempting to achieve comparable accuracy. In addition, in contrast to the currently used methods which introduce strict restrictions on the structure of the learned PBNs, the hypothesis space of our training paradigm is the set of all possible PBNs. Moreover, SCNFNs enable efficient sampling so as to statistically infer multistep transition probabilities which can provide information on the activity levels of individual nodes in the long run. Extensive experimental results showcase the scalability of the proposed approach both in terms of sample and runtime complexity. In addition, we provide examples to study large and complex cell signaling networks to show the potential of our model. Finally, we suggest several directions for future research on model variations, theoretical analysis, and potential applications of SCNFNs.