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Relative frequency is used to evaluate rules in the AQ program m-estimate of accuracy This accuracy estimate is biased toward the default accuracy expected of the rule It is often preferred when data is scarce and the rule must be evaluated based on few examples As above, let n and nc denote the number of examples matched and correctly predicted by the rule Let p be the prior probability that a randomly drawn example from the entire data set will have the classification assigned by the rule (eg, if 12 out of 100 examples have the value predicted by the rule, then p = 12) Finally, let m be the weight, or equivalent number of examples for weighting this prior p The m-estimate of rule accuracy is

Note if m is set to zero, then the m-estimate becomes the above relative frequency estimate As m is increased, a larger number of examples is needed to override the prior assumed accuracy p The m-estimate measure is advocated by Cestnik and Bratko (1991) and has been used in some versions of the CN2 algorithm It is also used in the naive Bayes classifier discussed in Section 691 Entropy This is the measure used by the PERFORMANCE subroutine in the algorithm of Table 102 Let S be the set of examples that match the rule preconditions Entropy measures the uniformity of the target function values for this set of examples We take the negative of the entropy so that better rules will have higher scores

awakeFromNib, numberWithInt, NSNumber, and so on. If Xcode can find documentation for a symbol, it will display here. The Quick Help window provides more than just descriptions for a method. If sample code is available, or useful related documents, you will see those, too. Click back on colorWithCalibratedRed:. The title bar in this window has two small buttons at the top right. The button marked by a small h brings up the method declaration in a new code window, while the button with a small book image takes you to the Class Reference page for that method in the documentation window (this is one of the points where you need to be connected to the Net). You can see from the method description that all of its arguments are floats and that it expects values between 0 and 1 (which was where the application came to grief, you will recall). You will be looking at the documentation window in more detail shortly, so just close it for the moment. The Quick Help window also shows links to relevant sample code. Try Color Sampler. Up comes a window featuring the sample code for that application (see Figure 8-2).

-Entropy (S) =

How can we use the more-general-than partial ordering to organize the search for a hypothesis consistent with the observed training examples One way is to begin with the most specific possible hypothesis in H, then generalize this hypothesis each time it fails to cover an observed positive training example (We say that a hypothesis "covers" a positive example if it correctly classifies the example as positive) To be more precise about how the partial ordering is used, consider the FIND-Salgorithm defined in Table 23 To illustrate this algorithm, assume the learner is given the sequence of training examples from Table 21 for the EnjoySport task The first step of FINDS is to initialize h to the most specific hypothesis in H

Journal Articles I J M Magby New algorithms for signal processing and analysis Journal of Computer and System Sciences 21 (1995) 423 475 I Notes on constructive logic and implications for computer science Mathematical Structures in Computer Science 5 (1994) 162 183 I Numerical solutions of boundary value problems Mathematical Structures in Computer Science 3 (1993) 122 145 Book I Magby, Jamal Marquis Studies in Artificial Intelligence 3rd ed New York: Academia Press, 1992

From here you can open either the source code in the browser window or the whole project in Xcode. The Quick Help window is an extremely useful way to discover how the code you are interested in should be used.

Upon observing the first training example from Table 21, which happens to be a positive example, it becomes clear that our hypothesis is too specific In particular, none of the "0" constraints in h are satisfied by this example, so each is replaced by the next more general constraint {hat fits the example; namely, the attribute values for this training example

h -+(Sunny, Warm, Normal, Strong, Warm, Same)

Your installation of Xcode Developer Tools will have placed a vast set of useful documentation and code samples on your computer, together with links to an even

This h is still very specific; it asserts that all instances are negative except for the single positive training example we have observed Next, the second training example (also positive in this case) forces the algorithm to further generalize h, this time substituting a " ' in place of any attribute value in h that is not satisfied by the new example The refined hypothesis in this case is

h -+(Sunny,Warm, , Strong, Warm, Same)