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I realise that similar questin is asked here also Softmax regression or $K$ binary logistic regression

But my concern is related to last section of this article from stanford http://ufldl.stanford.edu/wiki/index.php/Softmax_Regression It says decision will depend on mutual exclusivity of classes and if they are mutual exclusive then prefer softmax else k binary classifiers.

Can anyone provide any rigorous explanation for that statement directly relating the criteria of mutual exclusivity of classes to the performance of algorithm, because that article only has given just one line explanation : "This way, for each new musical piece(each class), your algorithm can separately decide whether it falls into each of the four categories."

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  • $\begingroup$ softmax produces a probability distribution vector: sum of its elements is 1 (i.e., it may confidently predict only a single category). This is a poor choice when you want a single example assigned multiple labels. $\endgroup$ – Alex Kreimer Nov 11 at 15:05

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