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You also have the ability to do Ad Hoc Distribution, which is a mechanism by which you can distribute your application in a limited fashion via email or a website. The idea of this mechanism is to allow you to conduct beta testing with a nominated group of testers, or to distribute your application to a small nominated group of people. Each of the proposed beta testers or users needs to register their Unique Device Identifier (UDID) in your Ad Hoc Distribution profile. You register these UDIDs at the iPhone Developer Program Portal. From this you will be able to download an updated .mobileprovision file, which allows you to distribute your application to the iPhones with these UDIDs. You can currently store up to 100 UDIDs in your profile, which limits the number of beta testers you can have.

2000 2002 SPRACHKENNTNISSE Deutsch: Englisch: Franz sisch:

E ( 6 ) is simply half the squared difference between the target output t and the d h e a r unit output od, summed over all training examples Here we characterize E as a function of 27, because the linear unit output o depends on this weight vector Of course E also depends on the particular set of training examples, but

we assume these are fixed during training, so we do not bother to write E as an explicit function of these 6 provides a Bayesian justification for choosing this particular definition of E In particular, there we show that under certain conditions the hypothesis that minimizes E is also the most probable hypothesis in H given the training data

If this is of interest to you, take a look at Erica Sadun s Ad Hoc Helper (free from the App Store). This tool makes it easier for your beta users to get their UDIDs to you.

To understand the gradient descent algorithm, it is helpful to visualize the entire hypothesis space of possible weight vectors and their associated E values, as illustrated in Figure 44 Here the axes wo and w l represent possible values for the two weights of a simple linear unit The wo, w l plane therefore represents the entire hypothesis space The vertical axis indicates the error E relative to some fixed set of training examples The error surface shown in the figure thus summarizes the desirability of every weight vector in the hypothesis space (we desire a hypothesis with minimum error) Given the way in which we chose to define E, for linear units this error surface must always be parabolic with a single global minimum The specific parabola will depend, of course, on the particular set of training examples

FIGURE 44 Error of different hypotheses For a linear unit with two weights, the hypothesis space H is the wg, w l plane The vertical axis indicates t error of the corresponding weight vector hypothesis, k relative to a fixed set of training examples The arrow shows the negated gradient at one particular point, indicating the direction in the wo, w l plane producing steepest descent along the error surface

Summary

Gradient descent search determines a weight vector that minimizes E by starting with an arbitrary initial weight vector, then repeatedly modifying it in small steps At each step, the weight vector is altered in the direction that produces the steepest descent along the error surface depicted in Figure 44 This process continues until the global minimum error is reached

How can we calculate the direction of steepest descent along the error surface This direction can be found by computing the derivative of E with respect to each component of the vector 2 This vector derivative is called the gradient of E with respect to 221, written ~ ~ ( i i r )

Beginnings and endings are important. You started your journey through this book, perhaps, as a newcomer to development using Xcode Tools. I hope that it is ending with you as an enthusiast for using these tools to create exciting new products for Mac OS X or the iPhone. They are truly excellent platforms for development, and if you get it right you will find a ready and willing user base for your software. I wish you well, and I hope that you use what you have learned in these pages to create effective, usable, well-tested, accessible, and, above all, enjoyable programs. If you have questions or comments about the book, please feel free to send them to feedback@learnxcodebook.com or leave feedback at the Apress website, www.apress.com.

Andr Michel1 N le 08/02/70 560, Rue de la R volution 95110 SANNOIS France T l phone: 496388261 E-mail: andr michel@lapostenet

Notice VE(221)is itself a vector, whose components are the partial derivatives of E with respect to each of the wi When interpreted as a vector in weight space, the gradient specijies the direction that produces the steepest increase in E The negative of this vector therefore gives the direction of steepest decrease For example, the arrow in Figure 44 shows the negated gradient -VE(G) for a particular point in the wo,wl plane Since the gradient specifies the direction of steepest increase of E, the training rule for gradient descent is