## Learning Bayesian network structure from correlation-immune data

Searching the complete space of possible Bayesian networks is intractable for problems of interesting size, so Bayesian network structure learning algorithms, such as the commonly used Sparse Candidate algorithm, employ heuristics. However, these heuristics also restrict the types of relationships that can be learned exclusively from data. They are unable to learn relationships that exhibit "correlation-immunity", such as parity. To learn Bayesian networks in the presence of correlation-immune relationships, we extend the Sparse Candidate algorithm with a technique called "skewing". This technique uses the observation that relationships that are correlation-immune under a speci c input distribution may not be correlation-immune under another, su ciently di erent distribution. We show that by extending Sparse Candidate with this technique we are able to discover relationships between random variables that are approximately correlation-immune, with a signi cantly lower computational cost than the alternative of considering multiple parents of a node at a time.

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*Proceedings of the 23rd Conference on Uncertainty in Artificial Intelligence, UAI 2007*(pp. 235–242).

*Proceedings of the 23rd Conference on Uncertainty in Artificial Intelligence, UAI 2007*, 235–42, 2007.

*Proceedings of the 23rd Conference on Uncertainty in Artificial Intelligence, UAI 2007*, 2007, pp. 235–42.