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Is it correct to argue that the Bayer Classifier is an ideal classifier, which is taken as a model by every other implemented classifier?

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Yes, this is correct, the Bayes Classifier is in fact theoretically optimal too. You can quite easily verify this, this is a link to the proof for the answer (https://cs.stackexchange.com/questions/72295/showing-that-bayes-classifier-is-optimal)

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