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In the scenario that I have a binary classification problem, and use a binary classifier to train and test my model, assuming everything else is constant, would using a multi-class classifier with 2 labels (one vs. all) produce the same results? (I know I should use the binary classifier, but I'm simply curious).

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"Binary classification" is simply multi-class classification with 2 labels. However, several classification algorithms are designed specifically for the 2-class problem, where the response is modeled as the outcome of a Bernouilli trial.

Of course, this can be generalized to the n-dimensional setting by modeling as the outcome of a multinomial sample. For instance logistic regression can be generalized to multinomial logistic regression.

Some models, such as decision trees and ensembles of trees, can take a different form however when applied to n-class classification.

So the answer is highly dependent on the implementation of the algorithm you're using. But the baseline answer is that any multiclass classification algorithms can be used for 2-class classification, and most 2-class classification algorithms can be generalized for multi-class classification.

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  • $\begingroup$ Wouldn't accuracy take a hit? (for multi-class classification). Also, is there a reasonable number of classes beyond which it might be a better idea to have a wide array of binary classifiers to get the same job done? $\endgroup$ – user799188 Jul 21 '15 at 0:37
  • $\begingroup$ You mean predicting each of the outcomes "is of class X" vs "is not of class X" ? this would be disastrous, as you would 1) find probabilities which do not normalize, 2) possibly have several "positive" classifications; 3) remove all the correlation structure between the various classes for prediction, thus actually increasing inaccuracy ; 4) have variance individual to each model rather than a single model, which usually means larger variance in final output $\endgroup$ – Youloush Jul 23 '15 at 15:23

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