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I want to use Data Mining/Machine Learning for a problem and I'm not sure if there is a standard algorithm for my problem.

The problem is as follows: There is a set of Events and a set of Potential Triggers. Each trigger can give rise to none, one or several Events. I want to classify Potential Triggers based on their features into ones that do not cause any event and ones that do. So far this is a standard classification task. Now comes the twist: For some of the Events, there are multiple Potential Triggers. This usually means that one is the real trigger and the others have been labeled accidentally. If the algorithm generates a rule (assuming rule learning for the moment) that covers one of the potential triggers for an event, this event shall be considered "explained" so that the other potential triggers for this event do not have to be classified as triggers for this event any more.

The twist in the problem smells a bit like set cover (https://en.wikipedia.org/wiki/Set_cover_problem), so I'm wondering if there is a good algorithm at all.

Is there a published algorithm? And does my problem have a standard name under which I can search for further information?

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I did not find an existing algorithm, but I have since published an algorithm for "set cover rule mining" myself. It is called GIMO: https://doi.org/10.1016/j.eswax.2020.100040

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It might be framed as multi-label classification with the constraint that "winner take all" for certain labels.

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