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Sorry for the convoluted question, I'm sure there is a better way to phrase this. Basically, say I have a 5-class target vector, but I'm only interested in membership in a subset of the classes.

For example, classes = A,B,C,D,E and I'm interested in (A or B) vs. (C or D or E). Is it better to 'recode' the labels in the training so that (A or B) = 1 and (C or D or E) = -1 and treat the problem as a binary classification. Or is there a benefit to modeling the classes separately and assign based on P(A or B) vs P(C or D or E)?

To put it concretely, say I'm trying to determine if a patient has cancer and I have a sample of patients with the type of cancer included if they have it. Is it better to model the chance of lymphoma, leukemia, etc. and aggregate for the chance of cancer, or to label all types as just cancer and model where the type is not distinguished.

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It's better to recode the labels. In general, it's more sample efficient to train a machine directly for the task-at-hand.

In the recoded case, the classifier would just need to estimate the a single separating hyperplane. In the other case, you are expecting a classifier to accurately estimate multiple hyperplanes. With finite samples, the latter is more prone to error because it's a harder task.

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