Although we can build a belief network starting from any ordering of its variables, its structure depends heavily on the ordering being selected: the topology of the network, and therefore the number of conditional independence relationships that may be explicitly represented can vary greatly from one ordering to another. We develop an algorithm for learning belief networks composed of two main subprocesses: (a) an algorithm that estimates a causal ordering and (b) an algorithm for learning a belief network given the previous ordering, each one working over different search spaces, the ordering and dag space respectively.
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