Finding the optimal Bayesian network given a constraint graph

Jacob Schreiber

doi:10.7717/peerj-cs.122

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Finding the optimal Bayesian network given a constraint graph

2017-07-03

Jacob Schreiber *

William Stafford Noble

DOI：10.7717/peerj-cs.122

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Abstract

En 中文

Despite recent algorithmic improvements, learning the optimal structure of a Bayesian network from data is typically infeasible past a few dozen variables. Fortunately, domain knowledge can frequently be exploited to achieve dramatic computational savings, and in many cases domain knowledge can even make structure learning tractable. Several methods have previously been described for representing this type of structural prior knowledge, including global orderings, super-structures, and constraint rules. While super-structures and constraint rules are flexible in terms of what prior knowledge they can encode, they achieve savings in memory and computational time simply by avoiding considering invalid graphs. We introduce the concept of a constraint graph as an intuitive method for incorporating rich prior knowledge into the structure learning task. We describe how this graph can be used to reduce the memory cost and computational time required to find the optimal graph subject to the encoded constraints, beyond merely eliminating invalid graphs. In particular, we show that a constraint graph can break the structure learning task into independent subproblems even in the presence of cyclic prior knowledge. These subproblems are well suited to being solved in parallel on a single machine or distributed across many machines without excessive communication cost.

Keywords:

Bayesian network

Structure learning

Discrete optimization

Parallel processing

Big data