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where P(c) is an abbreviation of P(C = c) etc. With this measure it is easy to detect that, in the example distribution of Figure 3.11 on page 75, the attributes A and C are conditionally independent given the attribute B. If we are not given a probability distribution (as we have assumed up to now), but instead a database of sample cases, it is clear that we have to estimate the conditioned joint distributions of the attributes, for which we want to test whether they are conditionally independent. Of course, this can lead to problems if the order of the tests is large, where the order of a conditional independence test is the number of conditioning attributes. If the number of conditioning attributes is large, there may be too few tuples having certain instantiation of these attributes to estimate reliably the conditioned joint distribution of the two test attributes. Actually this is a serious drawback of this method, although there are heuristic approaches to amend it (cf. Section 7.3), like, for instance, fixing an upper bound for the order of the tests to be carried out and assuming that all tests of higher order will fail if all tests with an order up to this bound failed. Finally, let us consider the third approach to learning a graphical model, which is based on measuring only the strengths of (marginal) dependences. As in the relational case, we may use the same measure as for the (approximate) independence tests. For the simple example discussed above we may apply the Kruskal algorithm with mutual information providing the edge weights (cf. Figure 7.6). This leads to a construction of graph 5 of Figure 7.5, in agreement with the results of the other two learning methods. asp.net ean 13 EAN - 13 ASP . NET Control - EAN - 13 barcode generator with free ...
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