Bayes Minimum Error Rate Classification
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categories is known perfectly. While this sort of stiuation rarely occurs in practice, it permits us to determine the optimal (Bayes) classifier against which we can compare all other classifiers. Moreover, in some bayes error rate in r problems it enables us to predict the error we will get when we generalize
Bayes Error Rate Example
to novel patterns. This approach is based on quantifying the tradeoffs between various classification decisions using probability and the costs minimum error rate classification in pattern recognition that accompany such decisions. It makes the assumption that the decision problem is posed in probabilistic terms, and that all of the relevant probability values are known. Let us reconsider the hypothetical problem
Bayes Decision Rule Example
posed in Chapter 1 of designing a classifier to separate two kinds of fish: sea bass and salmon. Suppose that an observer watching fish arrive along the conveyor belt finds it hard to predict what type will emerge next and that the sequence of types of fish appears to be random. In decision-theoretic terminology we would say that as each fish emerges nature is in one or the bayes decision boundary example other of the two possible states: Either the fish is a sea bass or the fish is a salmon. We let w denote the state of nature, with w = w1 for sea bass and w = w2 for salmon. Because the state of nature is so unpredictable, we consider w to be a variable that must be described probahilistically. Figure 4.1: Class conditional density functions show the probabiltiy density of measuring a particular feature value x given the pattern is in category wi. If the catch produced as much sea bass as salmon, we would say that the next fish is equally likely to be sea bass or salmon. More generally, we assume that there is some prior probability P(w1) that the next fish is sea bass, and some prior probability P(w2) that it is salmon. If we assume there are no other types of fish relevant here, then P(w1)+ P(w2)=1. These prior probabilities reflect our prior knowledge of how likely we are to get a sea bass or salmon before the fish actually appears. If we are forced to make a decision about the type of fish that will appear next just by using the valu
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