barcode in vb.net 2010 How Can Partially Learned Concepts Be Used in Software

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263 How Can Partially Learned Concepts Be Used
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Suppose that no additional training examples are available beyond the four in our example above, but that the learner is now required to classify new instances that it has not yet observed Even though the version space of Figure 23 still contains multiple hypotheses, indicating that the target concept has not yet been fully learned, it is possible to classify certain examples with the same degree of confidence as if the target concept had been uniquely identified To illustrate, suppose the learner is asked to classify the four new instances shown in Table 26 Note that although instance A was not among the training examples, it is classified as a positive instance by every hypothesis in the current version space (shown in Figure 23) Because the hypotheses in the version space unanimously agree that this is a positive instance, the learner can classify instance A as positive with the same confidence it would have if it had already converged to the single, correct target concept Regardless of which hypothesis in the version space is eventually found to be the correct target concept, it is already clear that it will classify instance A as a positive example Notice furthermore that we need not enumerate every hypothesis in the version space in order to test whether each
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CHAPTER 2 CONCEPT LEARNING AND THE GENERAL-TO-SPECIFIC ORDERING
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Instance A
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TABLE 26 New instances to be classified
classifies the instance as positive This condition will be met if and only if the instance satisfies every member of S (why ) The reason is that every other hypothesis in the version space is at least as general as some member of S By our definition of more-general~han, the new instance satisfies all members of S it if must also satisfy each of these more general hypotheses Similarly, instance B is classified as a negative instance by every hypothesis in the version space This instance can therefore be safely classified as negative, given the partially learned concept An efficient test for this condition is that the instance satisfies none of the members of G (why ) Instance C presents a different situation Half of the version space hypotheses classify it as positive and half classify it as negative Thus, the learner cannot classify this example with confidence until further training examples are available Notice that instance C is the same instance presented in the previous section as an optimal experimental query for the learner This is to be expected, because those instances whose classification is most ambiguous are precisely the instances whose true classification would provide the most new information for refining the version space Finally, instance D is classified as positive by two of the version space hypotheses and negative by the other four hypotheses In this case we have less confidence in the classification than in the unambiguous cases of instances A and B Still, the vote is in favor of a negative classification, and one approach we could take would be to output the majority vote, perhaps with a confidence rating indicating how close the vote was As we will discuss in 6, if we assume that all hypotheses in H are equally probable a priori, then such a vote provides the most probable classification of this new instance Furthermore, the proportion of hypotheses voting positive can be interpreted as the probability that this instance is positive given the training data
27 INDUCTIVE BIAS
As discussed above, the CANDIDATE-ELIMINATION algorithm will converge toward the true target concept provided it is given accurate training examples and provided its initial hypothesis space contains the target concept What if the target concept is not contained in the hypothesis space Can we avoid this difficulty by using a hypothesis space that includes every possible hypothesis How does the
size of this hypothesis space influence the ability of the algorithm to generalize to unobserved instances How does the size of the hypothesis space influence the number of training examples that must be observed These are fundamental questions for inductive inference in general Here we examine them in the context of the CANDIDATE-ELIMINATION algorithm As we shall see, though, the conclusions we draw from this analysis will apply to any concept learning system that outputs any hypothesis consistent with the training data
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