We present a hybrid constraint-based/Bayesian algorithm for learning causal networks in the presence of sparse data. The algorithm searches the space of equivalence classes of models (essential graphs) using a heuristic based on conventional constraint-based techniques. Each essential graph is then converted into a directed acyclic graph and scored using a Bayesian scoring metric. Two variants of the algorithm are developed and tested using data from randomly generated networks of sizes from 15 to 45 nodes with data sizes ranging from 250 to 2000 records. Both variations are compared to, and found to consistently outperform two variations of greedy search with restarts.

Constraint-based (CB) learning is a formalism for learning a causal network with a database D by performing a series of conditional-independence tests to infer structural information. This paper considers a new test of independence that combines ideas from Bayesian learning, Bayesian network inference, and classical hypothesis testing to produce a more reliable and robust test. The new test can be calculated in the same asymptotic time and space required for the standard tests such as the chi-squared test, but it allows the specification of a prior distribution over parameters and can be used when the database is incomplete. We prove that the test is correct, and we demonstrate empirically that, when used with a CB causal discovery algorithm with noninformative priors, it recovers structural features more reliably and it produces networks with smaller KL-Divergence, especially as the number of nodes increases or the number of records decreases. Another benefit is the dramatic reduction in the probability that a CB algorithm will stall during the search, providing a remedy for an annoying problem plaguing CB learning when the database is small.

Early, reliable detection of disease outbreaks is a critical problem today. This paper reports an investigation of the use of causal Bayesian networks to model spatio-temporal patterns of a non-contagious disease (respiratory anthrax infection) in a population of people. The number of parameters in such a network can become enormous, if not carefully managed. Also, inference needs to be performed in real time as population data stream in. We describe techniques we have applied to address both the modeling and inference challenges. A key contribution of this paper is the explication of assumptions and techniques that are sufficient to allow the scaling of Bayesian network modeling and inference to millions of nodes for real-time surveillance applications. The results reported here provide a proof-of-concept that Bayesian networks can serve as the foundation of a system that effectively performs Bayesian biosurveillance of disease outbreaks.