By Jeffrey Rosenberg
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7 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?
1). Instances for which c ( x ) = 1 are called positive examples, or members of the target concept. Instances for which C ( X ) = 0 are called negative examples, or nonmembers of the target concept. We will often write the ordered pair ( x ,c ( x ) ) to describe the training example consisting of the instance x and its target concept value c ( x ) . We use the symbol D to denote the set of available training examples. Given a set of training examples of the target concept c , the problem faced by the learner is to hypothesize, or estimate, c .
4 = 5 120 syntactically distinct hypotheses within H. Notice, however, that every hypothesis containing one or more "IZI" symbols represents the empty set of instances; that is, it classifies every instance as negative. Therefore, the number of semantically distinct hypotheses is only 1+ ( 4 . 3 . 3 . 3 . 3 . 3 )= 973. Our EnjoySport example is a very simple learning task, with a relatively small, finite hypothesis space. Most practical learning tasks involve much larger, sometimes infinite, hypothesis spaces.