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Artificial intelligence Learning symbolic representations of concepts Machine learning as a search problem Learning as an approach to improving problem solving Using prior knowledge together with training data to guide learning Bayesian methods Bayes' theorem as the basis for calculating probabilities of hypotheses The naive Bayes classifier Algorithms for estimating values of unobserved variables Computational complexity theory Theoretical bounds on the inherent complexity of different learning tasks, measured in terms of the computational effort, number of training examples, number of mistakes, etc required in order to learn Control theory Procedures that learn to control processes in order to optimize predefined objectives and that learn to predict the next state of the process they are controlling Information theory Measures of entropy and information content Minimum description length approaches to learning Optimal codes and their relationship to optimal training sequences for encoding a hypothesis Philosophy Occam's razor, suggesting that the simplest hypothesis is the best Analysis of the justification for generalizing beyond observed data Psychology and neurobiology The power law of practice, which states that over a very broad range of learning problems, people's response time improves with practice according to a power law Neurobiological studies motivating artificial neural network models of learning Statistics Characterization of errors (eg, bias and variance) that occur when estimating the accuracy of a hypothesis based on a limited sample of data Confidence intervals, statistical tests

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

window and click the Open... button. This shows two tabs (see Figure 12 22), giving access to a more useful hierarchical view.

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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.