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Equation (72) is important because it tells us how many training examples suffice to ensure (with probability (1 -6)) that every hypothesis in H having zero training error will have a true error of at most E Unfortunately, if H does not contain the target concept c, then a zero-error hypothesis cannot always be found In this case, the most we might ask of our learner is to output the hypothesis from H that has the minimum error over the training examples A learner that makes no assumption that the target concept is representable by H and that simply finds the hypothesis with minimum training error, is often called an agnostic learner, because it makes no prior commitment about whether or not C g H Although Equation (72) is based on the assumption that the learner outputs a zero-error hypothesis, a similar bound can be found for this more general case in which the learner entertains hypotheses with nonzero training error To state this precisely, let D denote the particular set of training examples available to the learner, in contrast to D,which denotes the probability distribution over the entire set of instances Let errorD(h) denote the training error of hypothesis h In particular, e r r o r ~ ( h ) defined as the fraction of the training examples in is D that are misclassified by h Note the errorD(h) over the particular sample of training data D may differ from the true error errorv(h) over the entire probability ) distribution 2 Now let hb,,, denote the hypothesis from H having lowest training error over the training examples How many training examples suffice to ensure (with high probability) that its true error errorD(hb,,,) will be no more than E errorg (hbest) Notice the question considered in the previous section is just a special case of this question, when errorD(hb,,) happens to be zero This question can be answered (see Exercise 73) using an argument analogous to the proof of Theorem 71 It is useful here to invoke the general Hoeffding bounds (sometimes called the additive Chernoff bounds) The Hoeffding bounds characterize the deviation between the true probability of some event and its observed frequency over m independent trials More precisely, these bounds apply to experiments involving m distinct Bernoulli trials (eg, m independent flips of a coin with some probability of turning up heads) This is exactly analogous to the setting we consider when estimating the error of a hypothesis in 5: The.

DVD-Audio is a separate application format from DVD-Video The DVDAudio specification includes different data types and features (see Table 638), with content stored in a separate audio zone on the disc (the AUDIO_TS directory) (see Figure 65) The DVD-Audio format includes a subset of DVD-Video features to provide onscreen menus and motion video DVD-Audio discs that include video are sometimes called DVD-AudioV discs Understanding the DVD-Audio specification first requires understanding the basics of the DVD-Video specification, since DVD-Audio inherits much of the architecture and navigation features of DVD-Video Any use of video with the audio also depends on the DVD-Video format This section of the book generally describes the parts of DVD-Audio that are new or different Other features, such as karaoke and text data, are essentially the same for both formats, so they are only described in the preceding DVDVideo section

After creating the data object, create an NSKeyedArchiver, passing the newly created data object as a parameter

TABLE 1 11 An analytical learning problem: SafeToStack(x,y)

5 to 60 C (41 to 140 F)

NSKeyedArchiver * archiver = [[NSKeyedArchiver alloc] initForWritingWithMutableData:theData];

3 to 85%

As shown in Table 111, we have chosen a hypothesis space H in which each hypothesis is a set of first-order if-then rules, or Horn clauses (throughout this chapter we follow the notation and terminology for first-order Horn clauses summarized in Table 103) For instance, the example Horn clause hypothesis shown in the table asserts that it is SafeToStack any object x on any object y, if the Volume of x is LessThan the Volume of y (in this Horn clause the variables v x and vy represent the volumes of x and y, respectively) Note the Horn clause hypothesis can refer to any of the predicates used to describe the instances, as well as several additional predicates and functions A typical positive training example, SafeToStack(Obj1, O b j 2 ) , is also shown in the table To formulate this task as an analytical learning problem we must also provide a domain theory sufficient to explain why observed positive examples satisfy the target concept In our earlier chess example, the domain theory corresponded to knowledge of the legal moves in chess, from which we constructed explanations

After initializing the NSKeyedArchiver, encode the objects to archive If you wish, you can encode multiple objects using the same archiver, provided all archived objects adopt the NSCoding protocol The following code snippet illustrates

5 to 55 C (23 to 131 F)