Bottom line: learning is a race between the amount of data you have and the number of hypotheses you consider. More data exponentially reduces the number of hypotheses that survive, but if you start with a lot of them, you may still have some bad ones left at the end. As a rule of thumb, if the learner only considers an exponential number of hypotheses (for example, all possible conjunctive concepts), then the data’s exponential payoff cancels it and you’re OK, provided you have plenty of examples and not too many attributes. On the other hand, if it considers a doubly exponential number (for
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