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The interface is familiar basically the same Interface Builder as the one you d load if you were building a Mac OS X application. However there are some immediate differences: The window is a fixed size (the size of the iPhone window, 320 460 pixels), the parameters available in each of the Inspector tabs are slightly different to suit the needs of an iPhone application, and the controllers in the Library window have a golden background color instead of blue on green. Actually, the main differences you will notice are in the Library window. The tools available are tailored to the iPhone: Web View, Map View, Picker View, and so on. You will be making more use of these later on in the book. Now, add some controls in the Main View window. We re looking for two TextFields but here is an interesting difference. The Label control is not an instance of an NSTextField, but rather a UILabel. Similarly, the Rounded Rect Button that sits next to it is a UIButton and the Text Field that will be used to input text is a UITextField. Clearly you are going to need to do some tweaking in the code to accommodate these, since the code refers to NSTextFields. That was the deliberate mistake I asked you to make a little way back: simply put, you can t just cut and paste even for simple examples, since user interface objects may not have the same names or behaviors. Flip back to Xcode and fix those now. Open MainViewController.h and edit the code to match the bold text in Listing 4 5.

24(k + log, n)

which proves the theorem To summarize, the above theorem states that the number of mistakes made by the WEIGHTED-MAJORITY algorithm will never be greater than a constant factor times the number of mistakes made by the best member of the pool, plus a term that grows only logarithmically in the size of the pool This theorem is generalized by Littlestone and Warmuth (1991), who show 3 that for an arbitrary 0 5 j < 1 the above bound is

Listing 4 5. Making the Changes to MainViewController.h #import "FlipsideViewController.h" @interface MainViewController : UIViewController <FlipsideViewControllerDelegate> { IBOutlet UILabel *destinationTextField; IBOutlet UITextField *sourceTextField; } - (IBAction)showInfo; - (IBAction)sayHello:(id)sender; @end

The main points of this chapter include:

The probably approximately correct (PAC) model considers algorithms that learn target concepts from some concept class C, using training examples drawn at random according to an unknown, but fixed, probability distribution It requires that the learner probably (with probability at least [ l - 61) learn a hypothesis that is approximately (within error E) correct, given computational effort and training examples that grow only polynornially with I/ , 1/6, the size of the instances, and the size of the target concept Within the setting of the PAC learning model, any consistent learner using H will, with probability (1 - S), a finite hypothesis space H where C output a hypothesis within error E of the target concept, after observing m randomly drawn training examples, as long as

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Basically you are changing the two NSTextField references into respectively UILabel and UITextField references. Double-check to ensure you have them the right way around it didn t matter for Mac OS X since the objects are both NSTextFields, but it matters now! Back in Interface Builder, drag UILabel, UIButton, and UITextField controls into the Main View window, and position them more or less as they are in Figure 4 5.

This gives a bound on the number of training examples sufficient for successful learning under the PAC model One constraining assumption of the PAC learning model is that the learner knows in advance some restricted concept class C that contains the target concept to be learned In contrast, the agnostic learning model considers the more general setting in which the learner makes no assumption about the class from which the target concept is drawn Instead, the learner outputs the hypothesis from H that has the least error (possibly nonzero) over the training data Under this less restrictive agnostic learning model, the learner is assured with probability (1 -6) to output a hypothesis within error E of the

The number of training examples required for successful learning is strongly influenced by the complexity of the hypothesis space considered by the learner One useful measure of the complexity of a hypothesis space H is its Vapnik-Chervonenkis dimension, VC(H) VC(H) is the size of the largest subset of instances that can be shattered (split in all possible ways) by H An alternative upper bound on the number of training examples sufficient for successful learning under the PAC model, stated in terms of VC(H) is