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Now we could attempt to estimate the two terms in Equation (619) based on the training data It is easy to estimate each of the P ( v j ) simply by counting the frequency with which each target value vj occurs in the training data However, estimating the different P(al, a 2 a,lvj) terms in this fashion is not feasible unless we have a very, very large set of training data The problem is that the number of these terms is equal to the number of possible instances times the number of possible target values Therefore, we need to see every instance in the instance space many times in order to obtain reliable estimates The naive Bayes classifier is based on the simplifying assumption that the attribute values are conditionally independent given the target value In other words, the assumption is that given the target value of the instance, the probability of observing the conjunction a l , a 2 a, is just the product of the probabilities for the individual attributes: P(a1, a2 a, 1 v j ) = P(ai lvj) Substituting this into Equation (619), we have the approach used by the naive Bayes classifier

Naive Bayes classifier:

You need to provide this with a binding to the Subscribers array controller, and particularly to the relationship called owners (since that s what we want ultimately to put.

POSTDOCTORAL AWARDS AND STUDIES The Mittag-Leffler Institute, 1991, Sweden Award: 100,000 Swedish crowns Studies: mathematical physics The Lettie Delilah Hensen Fellowship at Rhodes University, 1990, Grahamstown, South Africa Studied pure and applied mathematics

= argmax P (vj)

P (ai1vj)

in the list). So, select the acSubscribersForComputer controller and create a binding in the Controller Content (Content Set) section. Bind this controller to the acComputers controller, choosing selection as the Controller Key and owners as the Model Key Path (you will see that this is abbreviated to acComputers.selection.owners in the panel). Now I need somewhere to show the data in the user interface. Drag an NSTableView into the Computers window. Give this Table View two columns and bind the columns to the acSubscribersForComputer controller, choosing the Value section. Give Column 1 the binding acSubscribersForComputer.arrangedObjects.firstName and Column 2 the binding acSubscribersForComputer.arrangedObjects.lastName. That is it the user interface and all of the wiring is complete. Adding objects and bindings in this way can seem a little involved at first, but they are quite logical. You are ready to try out the application. To run the application, save the NIB file, return to Xcode, and choose Build and Go. You should see a running program something like Figure 5 11. You can see on the Computers tab the list of computer models and also the people who own the currently selected model.

(620)

where V N B denotes the target value output by the naive Bayes classifier Notice that in a naive Bayes classifier the number of distinct P(ailvj) terms that must

As you work with a data model in Core Data you may find yourself suddenly confronted with this error message on running the program:

be estimated from the training data is just the number of distinct attribute values times the number of distinct target values-a much smaller number than if we were to estimate the P(a1, a2 anlvj) terms as first contemplated To summarize, the naive Bayes learning method involves a learning step in which the various P(vj) and P(ai Jvj)terms are estimated, based on their frequencies over the training data The set of these estimates corresponds to the learned hypothesis This hypothesis is then used to classify each new instance by applying the rule in Equation (620) Whenever the naive Bayes assumption of conditional independence is satisfied, this naive Bayes classification VNB is identical to the MAP classification One interesting difference between the naive Bayes learning method and other learning methods we have considered is that there is no explicit search through the space of possible hypotheses (in this case, the space of possible hypotheses is the space of possible values that can be assigned to the various P(vj) and P(ailvj) terms) Instead, the hypothesis is formed without searching, simply by counting the frequency of various data combinations within the training examples

Let us apply the naive Bayes classifier to a concept learning problem we considered during our discussion of decision tree learning: classifying days according to whether someone will play tennis Table 32 from 3 provides a set of 14 training examples of the target concept PlayTennis, where each day is described by the attributes Outlook, Temperature, Humidity, and Wind Here we use the naive Bayes classifier and the training data from this table to classify the following novel instance: (Outlook = sunny, Temperature = cool, Humidity = high, Wind = strong) Our task is to predict the target value (yes or no) of the target concept PlayTennis for this new instance Instantiating Equation (620) to fit the current task, the target value VNB is given by