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space Other early concept learning systems include (Popplestone 1969; Michalski 1973; Buchanan 1974; Vere 1975; Hayes-Roth 1974) A very large number of algorithms have since been developed for concept learning based on symbolic representations 10 describes several more recent algorithms for concept learning, including algorithms that learn concepts represented in first-order logic, algorithms that are robust to noisy training data, and algorithms whose performance degrades gracefully if the target concept is not representable in the hypothesis space considered by the learner Version spaces and the CANDIDATE-ELIMINATION algorithm were introduced by Mitchell (1977, 1982) The application of this algorithm to inferring rules of mass spectroscopy is described in (Mitchell 1979), and its application to learning search control rules is presented in (Mitchell et al 1983) Haussler (1988) shows that the size of the general boundary can grow exponentially in the number of training examples, even when the hypothesis space consists of simple conjunctions of features Smith and Rosenbloom (1990) show a simple change to the representation of the G set that can improve complexity in certain cases, and Hirsh (1992) shows that learning can be polynomial in the number of examples in some cases when the G set is not stored at all Subramanian and Feigenbaum (1986) discuss a method that can generate efficient queries in certain cases by factoring the version space One of the greatest practical limitations of the CANDIDATEELIMINATION algorithm is that it requires noise-free training data Mitchell (1979) describes an extension that can handle a bounded, predetermined number of misclassified examples, and Hirsh (1990, 1994) describes an elegant extension for handling bounded noise in real-valued attributes that describe the training examples Hirsh (1990) describes an INCREMENTAL VERSION SPACE MERGING algorithm that generalizes the CANDIDATE-ELIMINATION algorithm to handle situations in which training information can be different types of constraints represented using version spaces The information from each constraint is represented by a version space and the constraints are then combined by intersecting the version spaces Sebag (1994, 1996) presents what she calls a disjunctive version space approach to learning disjunctive concepts from noisy data A separate version space is learned for each positive training example, then new instances are classified by combining the votes of these different version spaces She reports experiments in several problem domains demonstrating that her approach is competitive with other widely used induction methods such as decision tree learning and k-NEAREST NEIGHBOR.

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21 Explain why the size of the hypothesis space in the EnjoySport learning task is 973 How would the number of possible instances and possible hypotheses increase with the addition of the attribute Watercurrent, which can take on the values Light, Moderate, or Strong More generally, how does the number of possible instances and hypotheses grow with the addition of a new attribute A that takes on k possible values , I

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Those who are unfamiliar with the web probably think a rollover is a dog trick, but those who are web savvy know that a rollover occurs when a web page changes as the mouse cursor moves over and away from an object on the page Rollovers are used to make a dreary web page come alive, by altering its appearance as the visitor scans the contents of the web page with the mouse Any object on a web page can be changed with a rollover Some web developers change an image that is related to the object beneath the mouse cursor Other web developers pop up a new window that further describes the object The only limitation is your imagination In this chapter, you'll learn all about rollovers and how to implement rollovers in your own JavaScript applications

22 Give the sequence of S and G boundary sets computed by the CANDIDATE-ELIMINATION algorithm if it is given the sequence of training examples from Table 21 in reverse order Although the final version space will be the same regardless of the sequence of examples (why ), the sets S and G computed at intermediate stages will, of course, depend on this sequence Can you come up with ideas for ordering the training examples to minimize the sum of the sizes of these intermediate S and G sets for the H used in the EnjoySport example 23 Consider again the EnjoySport learning task and the hypothesis space H described in Section 22 Let us define a new hypothesis space H' that consists of all painvise disjunctions of the hypotheses in H For example, a typical hypothesis in H' is

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