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I want to estimate how many people are in a household by looking at account transactions. It would be also interesting to understand if in the household there are children.

I thought that a possible way to proceed could be to compare the living expenses with that of the average individual according to the national statistics. Moreover I could also perform text analytics to retrieve informations about what products people bought (in order to understand if they spent money to buy children products).

As model I could maybe use a random forest for classification (but please correct me if I'm wrong).

Are there better way to solve this problem?

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I think regression makes more sense here than classification; you are trying to predict a number. In particular I would recommend Poisson regression since you are modeling count data. Software is readily available for various languages.

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