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Bayesian learning methods are relevant to our study of machine learning for two different reasons First, Bayesian learning algorithms that calculate explicit probabilities for hypotheses, such as the naive Bayes classifier, are among the most practical approaches to certain types of learning problems For example, Michie et al (1994) provide a detailed study comparing the naive Bayes classifier to other learning algorithms, including decision tree and neural network algorithms These researchers show that the naive Bayes classifier is competitive with these other learning algorithms in many cases and that in some cases it outperforms these other methods In this chapter we describe the naive Bayes classifier and provide a detailed example of its use In particular, we discuss its application to the problem of learning to classify text documents such as electronic news articles

For such learning tasks, the naive Bayes classifier is among the most effective algorithms known The second reason that Bayesian methods are important to our study of machine learning is that they provide a useful perspective for understanding many learning algorithms that do not explicitly manipulate probabilities For example, in this chapter we analyze algorithms such as the FIND-S and CANDIDATEELIMINATION algorithms of 2 to determine conditions under which they output the most probable hypothesis given the training data We also use a Bayesian analysis to justify a key design choice in neural network learning algorithms: choosing to minimize the sum of squared errors when searching the space of possible neural networks We also derive an alternative error function, cross entropy, that is more appropriate than sum of squared errors when learning target functions that predict probabilities We use a Bayesian perspective to analyze the inductive bias of decision tree learning algorithms that favor short decision trees and examine the closely related Minimum Description Length principle A basic familiarity with Bayesian methods is important to understanding and characterizing the operation of many algorithms in machine learning Features of Bayesian learning methods include:

The first part covers the core Xcode toolset. 2 introduces the Xcode program itself, covering the Xcode Workspace and code-development tools. 3 describes Interface Builder and takes you through examples of interface development for different types of applications. In 4 you get your first look at the tools for iPhone development. I have already mentioned s 5 and 6, on Cocoa Frameworks and MVC. In 7 you will learn how to use the various debugging tools in Xcode. 8 explores Apple s Developer Documentation and other sources of help and support. The final chapter in this core section, 9, allows you to put into practice much of what you have learned in the preceding chapters, when you build an entire Mac OS X application.

Each observed training example can incrementally decrease or increase the estimated probability that a hypothesis is correct This provides a more flexible approach to learning than algorithms that completely eliminate a hypothesis if it is found to be inconsistent with any single example Prior knowledge can be combined with observed data to determine the final probability ~f a hypothesis In Bayesian learning, prior knowledge is provided by asserting (1) a prior probability for each candidate hypothesis, and (2) a probability distribution over observed data for each possible hypothesis Bayesian methods can accommodate hypotheses that make probabilistic predictions (eg, hypotheses such as "this pneumonia patient has a 93% chance of complete recovery") New instances can be classified by combining the predictions of multiple hypotheses, weighted by their probabilities Even in cases where Bayesian methods prove computationally intractable, they can provide a standard of optimal decision making against which other practical methods can be measured

One practical difficulty in applying Bayesian methods is that they typically require initial knowledge of many probabilities When these probabilities are not known in advance they are often estimated based on background knowledge, previously available data, and assumptions about the form of the underlying distributions A second practical difficulty is the significant computational cost required to determine the Bayes optimal hypothesis in the general case (linear in the number of candidate hypotheses) In certain specialized situations, this computational cost can be significantly reduced

This second part builds on the core tools to cover some more advanced and less-used features. 10 introduces revision control with Subversion, a subject avoided by many developers (me included until I had lost one piece of project code too many) but that, with a little investment, will ensure that you never again lose track of your precious code. In 11 we will be tackling another topic that is normally given a wide berth unit testing. Very few developers build unit tests, yet properly done they can be a considerable timesaver. Ruby on Rails developers, used to having unit tests built into the environment, will be familiar with the benefits of this approach. 12 takes covers performance monitoring and analysis tools if you ve ever wondered what Instruments is for and how to use it, this is the chapter for you.