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If we have a muli-label classification problem, is that true to train the model over each target separately? For example, if we have a 2-label(y1,y2) classification, once we train a model with y1 and simultaneously train another model with y2.

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Yes, before further explaination bare in mind there is a distinction between multi-class and multi-label models - but the idea of having multiple classifier can work in both scenario.

This is a common approach for multi-label prediction but not so usual for multi-class. Mainly because in multi-label, labels are not mutually exclusive. say if an observation x belong to N labels, you make N model where the goal is to predict if the observation belong to N_i where i is the index of the label.

Multi-label prediction is common in object recognition. For example in Yolo a common framework for multi-object recognition the output for each object is encoded like [1, x_center, y_center, width, height, [1, 0, 1, 0, 0]]. where the last binary list indicate which groups the object belongs to (in this case there are 5 possible objects).

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