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I have lots of transactional and demographic (etc.) data about my customers and I want to understand: "What are the characteristics (age, profession etc.) of valuable customers?"

To do this I was thinking about using an RFM model to determine the most valuable customers. I'd then use the RFM score (3-15) as the dependent variables in a supervised learning problem with demographics as the indepedent variables (likely using some treee based model). From this I would be able to look at feature importance to determine the key charateristics.

My concern with this is that I want to know which combinations of independent variables are corellated with high value customers. For example, while Female might not correlate with high-value, maybe all of my high-value customers are Female Nurses, while Male Nurses might not be valuable. In this case neither gender or profession specifically correlates to value, but a combination of the two does and I'd want to see relationship.

Based on my (limited) understanding, looking at feature importance in tree models would only look at the importance of individual features.

How can I capture the importance of a combination of independent variables? Would it require a specific type of supervised learning (boosted tree vs linear regression etc.)?

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