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The problem here is that with this very expressive hypothesis representation, the S boundary will always be simply the disjunction of the observed positive examples, while the G boundary will always be the negated disjunction of the observed negative examples Therefore, the only examples that will be unambiguously classified by S and G are the observed training examples themselves In order to converge to a single, final target concept, we will have to present every single instance in X as a training example! It might at first seem that we could avoid this difficulty by simply using the partially learned version space and by taking a vote among the members of the version space as discussed in Section 263 Unfortunately, the only instances that will produce a unanimous vote are the previously observed training examples For, all the other instances, taking a vote will be futile: each unobserved instance will be classified positive by precisely half the hypotheses in the version space and will be classified negative by the other half (why ) To see the reason, note that when H is the power set of X and x is some previously unobserved instance, then for any hypothesis h in the version space that covers x, there will be anoQer

You also need to have access to a good graphics package to create the basic image for your icon, and Apple doesn t supply one of those for free in the Xcode Tools (hey, what did you expect ). There are many great tools to choose from, including free tools such as the GIMP. I use Photoshop because I know my way around it. I ll just go through the process briefly here: obviously the detailed processes for image manipulation will vary from one image-editing application to another, so I won t go into unnecessary detail. I started with a stock image a photorealistic image of an open book with a pen. I made this image big enough to look good at 512 x 512 pixels, as this is the largest icon size used in Mac OS X. I used the various lasso tools to cut out the image from the background, and then added a drop shadow and some text. I shaped the text so that it followed more or less the curve of the page. This gave me the image shown in Figure 13 2.

hypothesis h' in the power set that is identical to h except for its classification of x And of course if h is in the version space, then h' will be as well, because it agrees with h on all the observed training examples

The above discussion illustrates a fundamental property of inductive inference: a learner that makes no a priori assumptions regarding the identity of the target concept has no rational basis for classifying any unseen instances In fact, the only reason that the CANDIDATE-ELIMINATION algorithm was able to generalize beyond the observed training examples in our original formulation of the EnjoySport task is that it was biased by the implicit assumption that the target concept could be represented by a conjunction of attribute values In cases where this assumption is correct (and the training examples are error-free), its classification of new instances will also be correct If this assumption is incorrect, however, it is certain that the CANDIDATE-ELIMINATION algorithm will rnisclassify at least some instances from X Because inductive learning requires some form of prior assumptions, or inductive bias, we will find it useful to characterize different learning approaches by the inductive biast they employ Let us define this notion of inductive bias more precisely The key idea we wish to capture here is the policy by which the learner generalizes beyond the observed training data, to infer the classification of new instances Therefore, consider the general setting in which an arbitrary learning algorithm L is provided an arbitrary set of training data D, = {(x,c(x))} of some arbitrary target concept c After training, L is asked to classify a new instance xi Let L(xi, D,) denote the classification (eg, positive or negative) that L assigns to xi after learning from the training data D, We can describe this inductive inference step performed by L as follows

Notice that I kept a layer with the original untouched image file. This is prudence born of experience it s always a good idea to leave the original and work on a copy, because you will make mistakes! Notice also that I have a layer that just provides a white background for the image. Since the icon will have transparency and shape, you can use a background layer here to make sure that you have properly cut out the original background and that the drop shadow works OK. Try a few different background colors. Having saved the Photoshop image, I exported it as a transparent Portable Network Graphics (PNG) file. This is a good format for bringing in to Icon Composer.