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ID3 in its pure form performs no backtracking in its search Once it,selects an attribute to test at a particular level in the tree, it never backtracks to reconsider this choice Therefore, it is susceptible to the usual risks of hill-climbing search without backtracking: converging to locally optimal solutions that are not globally optimal In the case of ID3, a locally optimal solution corresponds to the decision tree it selects along the single search path it explores However, this locally optimal solution may be less desirable than trees that would have been encountered along a different branch of the search Below we discuss an extension that adds a form of backtracking (post-pruning the decision tree) ID3 uses all training examples at each step in the search to make statistically based decisions regarding how to refine its current hypothesis This contrasts with methods that make decisions incrementally, based on individual training examples (eg, FIND-Sor CANDIDATE-ELIMINATION) One advantage of using statistical properties of all the examples (eg, information gain) is that the resulting search is much less sensitive to errors in individual training examples ID3 can be easily extended to handle noisy training data by modifying its termination criterion to accept hypotheses that imperfectly fit the training data

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.

What is the policy by which ID3 generalizes from observed training examples to classify unseen instances In other words, what is its inductive bias Recall from 2 that inductive bias is the set of assumptions that, together with the training data, deductively justify the classifications assigned by the learner to future instances Given a collection of training examples, there are typically many decision trees consistent with these examples Describing the inductive bias of ID3 therefore consists of describing the basis by which it chooses one of these consistent hypotheses over the others Which of these decision trees does ID3 choose It chooses the first acceptable tree it encounters in its simple-to-complex, hillclimbing search through the space of possible trees Roughly speaking, then, the ID3 search strategy (a) selects in favor of shorter trees over longer ones, and (b) selects trees that place the attributes with highest information gain closest to the root Because of the subtle interaction between the attribute selection heuristic used by ID3 and the particular training examples it encounters, it is difficult to characterize precisely the inductive bias exhibited by ID3 However, we can approximately characterize its bias as a preference for short decision trees over complex trees

Table 6-1