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Let's say I have a set of features: a, b, c, d, e, f. I'm now interested in identifying possible interactions between these features that best predict an outcome. For example, it could be that the features a, f, and the interactions a:b:g, d:f and c:e are the 5 most important factors that predict the outcome. It is not only important for an algorithm to account for feature interactions, but I also want to be able to identify these interactions.

How could I approach this problem with machine learning?

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Seems like you're looking for association rules. One example algorithm for recovering these is Apriori algorithm.

If you want a textbook that covers them, Mining Massive Datasets is one choice (Frequent Itemsets chapter - it contains lots of exercises).

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