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A tutorial on AdaBoost suggests that AdaBoost can be applied to a continuum of classifiers (at the bottom of the first page).

Does it mean to simply discretize the classifiers, for example, which are parameterized by one or two real number, or refer to a generalized version of AdaBoost theory, which may be capable of coping with the abstract classifier "space" (though everything should be discretized when put into practice)? I did some googling, but failed to find what I need. Can anyone provide some references?

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Adaboost works by fitting a weak classifier, such as a stumpy decision tree, reweighing the data to emphasize difficult cases, and repeating. Under some reasonable definitions, the number of possible trees is large but finite (you can only divide the data into two pieces in so many ways). But as your tutorial points out, that isnt an essential feature. Here's a paper that used neural nets as it's weak classifier, for example: http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.90.829&rep=rep1&type=pdf

The neural nets have continuous parameters, but that doesn't really affect the algorithm, and no discretization is needed. I suppose you could discretize it after the fact if that helped with interpretation, but it works fine with real numbers.

You should be able to find other examples with search terms like "boosted X," where X is a continuous classifier. Hope this helps!

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