An algorithm for automated construction of a sparse Bayesian network given an unstructured probabilis tic model and causal domain information from an expert has been developed and implemented. The goal is to obtain a network that explicitly reveals as much information regarding conditional indepen dence as possible. The network is built incrementally adding one node at a time. The expert's information and a greedy heuristic that tries to keep the number of arcs added at each step to a minimum are used to guide the search for the next node to add. The prob abilistic model is a predicate that can answer queries about independencies in the domain. In practice the model can be implemented in various ways. For ex ample, the model could be a statistical independence test operating on empirical data or a deductive prover operating on a set of independence statements about the domain. networks and influence diagrams. The problem of inducing a Bayesian network from empirical data and domain information can be viewed as consisting of two subproblems: The solution to the second subproblem requires build ing a structured model from an unstructured one. The work described in this paper concentrates on this structuring problem. In the context of the previous section, a more precise statement of the problem we are solving here is as follows. We are given: • A black box that can answer questions of the type "Is X independent of Y given Z?" where X, Y and Z are sets of variables in the domain. This could, for example, be a statistical test op erating on empirical data or a deductive prover that knows the basic probability model axioms and operates on a declarative set of indepen dence statements. • Some partial expert information about the do main. The expert may make the following kinds A is a cause of B declares that the ex pert views A as a direct predecessor of B in the belief network representation (see [3] ). Our goal is to build a sparse Bayesian network for the domain given the information above. In a model it is usually easy for an expert to identify some 'primary' causes and some observables. The flow of causality in a causal model is from these primary causes to the observables. For example, in the medical domain, these primary causes are diseases and the observables are symptoms. In a model of a machine the primary causes would be possible faults and the observables would be sensors. Hypothesis variables correspond to primary causes and evidence variables to observables. 2 The work described in this paper makes use of the terminology and results found in Pearl [3] . A brief summary of the relevant material follows. Probabilistic models comprise a class of depen
Srinivas et al. REF proposed an algorithm for the automatic construction of sparse Bayesian networks from information about the domain provided by an expert.
Automated Construction of Sparse Bayesian Networks from Unstructured Probabilistic Models and Domain Information
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