A Gentle Introduction to the Bayes Optimal Classifier

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Because the Bayes classifier is optimal, the Bayes error is the minimum possible error that can be made. Further, the model is often described in terms of classification, e.g. the Bayes Classifier. Nevertheless, the principle applies just as well to regression: that is, predictive modeling problems where a numerical value is predicted instead of a class label. It is a theoretical model, but it is held up as an ideal that we may wish to pursue. In theory we would always like to predict qualitative responses using the Bayes classifier. But for real data, we do not know the conditional distribution of Y given X, and so computing the Bayes classifier is impossible. Therefore, the Bayes classifier serves as an unattainable gold standard against which to compare other methods.

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