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about whether x is a positive or negative example; it only detennines the probability that x will be encountered The learning task is to learn the target concept or target function f by considering a space H of possible hypotheses Training examples of the target function f are provided to the learner by a trainer who draws each instance independently, according to the distribution D, and who then forwards the instance x along with its correct target value f ( x ) to the learner To illustrate, consider learning the target function "people who plan to purchase new skis this year," given a sample of training data collected by surveying people as they arrive at a ski resort In this case the instance space X is the space of all people, who might be described by attributes such as their age, occupation, how many times they skied last year, etc The distribution D specifies for each person x the probability that x will be encountered as the next person arriving at the ski resort The target function f : X + { O , 1 ) classifies each person according to whether or not they plan to purchase skis this year Within this general setting we are interested in the following two questions:

Well that was a simple example, and you may be thinking that it was quite a performance just to produce a simple message. The important thing to remember is that this process of defining the components, the messages and the connections between the components is the same for most of the applications you will write using the Xcode tools, and once you get into the swing of things it all happens very quickly. It is also easy to build on what you have already got: the beauty of object-oriented software development, and MVC approach in particular, is the ability to incrementally improve and add to your software. Let s do that now. Suppose you wanted, rather than just popping up Hello, World! every time, to create a message and then click the button to display that message in the label. It turns out to be quite straightforward. Here are the things you need to do: 1. There needs to be another outlet (the controller is going to need to communicate with a textField where you type the message let s call it sourceTextField). The sayHello: method needs tweaking so it picks up the contents of the sourceTextField rather than just Hello, World! . There needs to be a textField in the user interface window. The new sourceTextField outlet needs to connect to the textField in the interface.

random according to the distribution D, what is the best estimate of the accuracy of h over future instances drawn from the same distribution 2 What is the probable error in this accuracy estimate

To answer these questions, we need to distinguish carefully between two notions of accuracy or, equivalently, error One is the error rate of the hypothesis over the sample of data that is available The other is the error rate of the hypothesis over the entire unknown distribution D of examples We will call these the sample error and the true error respectively The sample error of a hypothesis with respect to some sample S of instances drawn from X is the fraction of S that it misclassifies:

2. 3. 4.

Definition: The sample error (denoted errors(h)) of hypothesis h with respect to target function f and data sample S is

Where n is the number of examples in S, and the quantity S(f ( x ) , h ( x ) ) is 1 if f ( x ) # h ( x ) , and 0 otherwise

Start by opening HelloController.h. You need to add a new outlet (the bold text in Listing 3 3 below):

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The true error of a hypothesis is the probability that it will misclassify a single randomly drawn instance from the distribution D

Definition: The true error (denoted e r r o r v ( h ) ) of hypothesis h with respect to target function f and distribution D,is the probability that h will misclassify an instance

Listing 3 3. Adding another outlet to HelloController.h #import <Cocoa/Cocoa.h> @interface HelloController : NSObject { IBOutlet NSTextField *destinationTextField; IBOutlet NSTextField *sourceTextField; } - (IBAction)sayHello:(id)sender; @end

errorv ( h ) = Pr [f ( x ) # h ( x ) ]

distribution V What we usually wish to know is the true error errorv(h) of the hypothesis, because this is the error we can expect when applying the hypothesis to future examples All we can measure, however, is the sample error errors(h) of the hypothesis for the data sample S that we happen to have in hand The main question considered in this section is "How good an estimate of errorD(h) is provided by errors (h) "

Next, open up HelloController.m. You need to modify the sayHello: method to look like this (see Listing 3 4; the line to change is in bold).