Characterization of Inclusion Neighbourhood in Terms of the Essential Graph: Uper Neighbours

نویسنده

  • Milan Studený
چکیده

The topic of the contribution is to characterize the inclusion neighbourhood of a given equivalence class of Bayesian networks in terms of the respective essential graph in such a way that it can be used eeciently in a method of local search for maximization of a quality criterion. One can distinguish two kinds of inclusion neighbours: upper and lower ones. A previous paper 15] gave a characterization of upper inclusion neighbourhood , and this contribution gives a characterization of lower inclusion neighbourhood. It is shown here that each inclusion neighbour is uniquely described by a pair ((a; b]; C) where a; b] is an unordered pair of distinct nodes and C N n fa; bg a disjoint set of nodes in the essential graph. The second basic result is that, for given a; b], the collection of those sets C which correspond to lower inclusion neighbours has a special form. More speciically, given an unordered pair a; b] of nodes which is not an edge in the essential graph, the respective collection of sets C is the union of (at most) two tufts of sets. The least and maximal sets of these two tufts, which determine them, can also be read from the essential graph. Some of the approaches to learning Bayesian networks use the method of max-imization of a quality criterion, named also 'quality measure' 3] and 'score metric' 4]. Quality criterion is a function, designed by a statistician, which ascribes a real number to data and a network. This number evaluates how the statistical model determined by the network is suitable to explain the occurence

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تاریخ انتشار 2003