What are some good error metrics for multi-label (not mutli-class) problem in industry?
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A common example is the Jaccard similarity coefficient:
$J(Y, P) = \frac{|Y~\cap~P|}{|Y~\cup~P|}$
where $P$ is the set of predicted labels for an instance and $Y$ is the true set of labels. This gives a value between $0$ and $1$ for each instance, which you can average over the whole test set to give a score. If $P = Y$, then $J(Y, P) = 1$.
This is implemented in scikit-learn as sklearn.metrics.jaccard_similarity_score.
