Data-driven learning of Boolean networks and functions by optimal causation entropy principle

Boolean functions, and networks thereof, are useful for analysis of complex data systems, including from biological systems, bioinformatics, decision making, medical fields, and finance. However, automated learning of a Boolean networked function, from data, is a challenging task due in part to the large number of unknown structures of the network and the underlying functions. In this paper, we develop a new information theoretic methodology, called Boolean optimal causation entropy, that we show is significantly more efficient than previous approaches. Our method is computationally efficient and also resilient to noise. Furthermore, it allows for selection of features that best explains the process, described as a networked Boolean function reduced-order model. We highlight our method to the feature selection in several real-world examples: (1) diagnosis of urinary diseases, (2) cardiac single proton emission computed tomography diagnosis, (3) informative positions in the game Tic-Tac-Toe, and (4) risk causality analysis of loans in default status.