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One effective approach to implementing LEARN-ONE-RULE organize the hyis to pothesis space search in the same general fashion as the ID3 algorithm, but to follow only the most promising branch in the tree at each step As illustrated in the search tree of Figure 101, the search begins by considering the most general rule precondition possible (the empty test that matches every instance), then greedily adding the attribute test that most improves rule performance measured over the training examples Once this test has been added, the process is repeated by greedily adding a second attribute test, and so on Like ID3, this process grows the hypothesis by greedily adding new attribute tests until the hypothesis reaches an acceptable level of performance Unlike ID3, this implementation of LEARN-ONERULE follows only a single descendant at each search step-the attribute-value pair yielding the best performance-rather than growing a subtree that covers all possible values of the selected attribute This approach to implementing LEARN-ONE-RULE performs a general-tospecific search through the space of possible rules in search of a rule with high accuracy, though perhaps incomplete coverage of the data As in decision tree learning, there are many ways to define a measure to select the "best" descendant To follow the lead of ID3 let us for now define the best descendant as the one whose covered examples have the lowest entropy (recall Equation f331) The general-to-specific search suggested above for the LEARN-ONE-RULE algorithm is a greedy depth-first search with no backtracking As with any greedy

You have seen most of what the Console has to offer already. It is a very useful place to see the output from NSLog messages as you saw earlier. Any errors that would normally go to stderr (a Unix convention providing a standard place to write error messages) would also appear here. If you should happen to be writing command line programs, you

A/\-----

FIGURE 101 The search for rule preconditions as LEARN-ONE-RULE proceeds from general to specific At each step, the preconditions of the best rule are specialized in all possible ways Rule postconditions are determined by the examples found to satisfy the preconditions This figure illustrates a beam search of width 1

can also use the Console for handling stdin and stdout traffic. In practice, I use the Console a lot for NSLog messages from my code and that is about it.

search, there is a danger that a suboptimal choice will be made at any step To reduce this risk, we can extend the algorithm to perform a beam search; that is, a search in which the algorithm maintains a list of the k best candidates at each step, rather than a single best candidate On each search step, descendants (specializations) are generated for each of these k best candidates, and the resulting set is again reduced to the k most promising members Beam search keeps track of the most promising alternatives to the current top-rated hypothesis, so that all of their successors can be considered at each search step This general to specific beam search algorithm is used by the CN2 program described by Clark and Niblett (1989) The algorithm is described in Table 102

L E A R N - O N E - R U L E ( TAttributes,~ ~ ~ ~ ~ ~ ~ U ~ ~ , ~ ~ ~ ~ Examples, k)

expert knowledge of mathematical theories of dynamical systems advanced knowledge of the application of computer decision-making models in the medical sciences full knowledge of software and hardware available for research in the natural sciences high value placed on teamwork, flexibility, and quality interpersonal communication strong analytical, conceptual, and organizational skills prompt in planning and implementing agreed-upon proposals and ideas

Summary

Returns a single rule that covers some of the Examples Conducts a generalJotospec$c greedy beam search for the best rule, guided by the PERFORMANCE metric Initialize Besthypothesis to the most general hypothesis 0 Initialize Candidatehypotheses to the set (Besthypothesis) While Candidatehypotheses is not empty, Do I Generate the next more spec@ candidatehypotheses a Allronstraints c the set of all constraints of the form (a = v ) , where a is a member of Attributes, and v is a value of a that occurs in the current set of Examples a Newrandidatehypotheses c for each h in Candidatehypotheses, for each c in Alll-onstraints, create a specialization of h by adding the constraint c a Remove from Newl-andidatehypotheses any hypotheses that are duplicates, inconsistent, or not maximally specific 2 Update Besthypothesis a For a l h in Newnandidatehypotheses do l a If PERFORMANCE(^, Examples, Targetattribute) z PERFORMANCE(Besthypothesis, Examples, Targetattribute)) Then Besthypothesis t h 3 Update Candidatehypotheses a Candidatehypotheses c the k best members of New-candidatehypotheses, according to the PERFORMANCE measure Return a rule of the form " F Best hypothesis THEN prediction" I where prediction is the most frequent value of Targetattribute among those Examples that match Besthypothesis

PERM)RMANCE(~, Examples, Target attribute) a hxxamples t the subset of Examples that match h return -Entropy(hxxarnples), where entropy is with respect to Targetattribute

This short chapter gave you a good idea of how to use the Xcode Debugger, and something of the benefits and drawbacks of the different approaches to using the Debugger in your projects. There was a brief introduction in this chapter on looking up documentation from within your code a very brief introduction to a very important topic, and one that is Xcode s best-kept secret: the developer documentation. That is where you are heading in the next chapter.