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Normally when I train a random forest to classify observations into multi-class buckets the objective is to correctly predict which bucket an observation will fall into based on historical (training) data.

Instead, I want to train the random forest to classify observations on some other criteria, such as profit maximization. Is this possible?

Here's an example:

Imagine that we have data on Dropbox subscriptions over the past 1 year. Some Dropbox leads (potential customers) had 1 of 3 possible coupons, other leads did not have a coupon.

In this scenario I want to determine which (if any) coupon I should should offer to a lead to maximize net revenue, considering their likelihood of purchasing a subscription, their predicted retention (# of months they will continue their subscription) and the effect of the coupon on purchase price.

Theoretically some leads who are likely to purchase a subscription and be retained will not need a coupon to do so. Others might produce higher net revenue from a coupon for "$5 off per month" or "first month free", etc.

I presume the dependent variable should still be coupon type, i.e.

Y = No Coupon, Coupon A, Coupon B, Coupon C, Coupon D

Is it possible to make the random forest work in this way? You can consider this question language-agnostic, though if I have a choice I will try to do this in R.

I know that in the case of eXtreme Gradient Boosting in either R or Python I can specify a custom objective function.

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Your target variable should always reflect what you're trying to optimize (maximize or reduce), so if you want to maximize revenue, you should make revenue your target variable. I would use the coupons as independent variables. When you want to see whether to offer a coupon or not for a particular customer, feed a new record into your model for every permutation of coupon / no coupon and see which has the highest prediction. There might be other/better ways of doing this, but I think this should get what you're looking for.

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  • $\begingroup$ But I'm trying to decide which coupon to offer based on profit maximization, allowing for individual level variation based on demographics and other data. $\endgroup$ – Hack-R Aug 9 '16 at 22:40
  • $\begingroup$ I know that in the case of eXtreme Gradient Boosting in either R or Python I can specify a custom objective function. This is just a different tree model, so I should be able to do the same, no? $\endgroup$ – Hack-R Aug 10 '16 at 3:08
  • $\begingroup$ @HackR I suppose, but that seems like a more indirect way of doing it. To me it sounds simpler to just use a default loss/objective function (like mean absolute error), and just make your target variable more relevant. By the way, you can use any model, not just tree models. $\endgroup$ – Ryan Zotti Aug 10 '16 at 12:46

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