# Finding feature values for regression model such that output is more than a given value?

Suppose you have an (online) shop. You have a dataset containing $$p$$ features (representing customer characteristics) $$X = (x_1, \ldots, x_p)$$ and a feature $$y$$, representing how much money a customer with given characteristics has spent in our shop previously.

You want to know which customers you need to target to increase profit. In other words, we want to know which customers are likely to spend a lot in our shop, so that we could target them through i.e. ads, special offers, etc.

I thought about translating this problem as follows:

Given the dataset, we can split it into a training/test dataset and fit some ML model, say $$\hat{f}(X)$$ (assuming for the moment that we can fit a model that has good enough predictive power). Then, to find customers that spend more than a given level, say $$c$$, we want to find those feature values $$(x_1 = k_1, \ldots, x_p = k_p)$$ such that $$\hat{f}(x_1 = k_1, \ldots, x_p = k_p) \geq c$$

I could find such candidates by e.g. genetic algorithms.

My question: is there a name for this type of approach?

• The condition $f(X)>c$ defines a region in feature space; this is very different than finding maximizers. The function $f(X)$ doesn't have to be bounded at all (and most likely isn't) so maximizers don't necessarily exist, or they might represent unrealistic customer characteristics. May 14 at 9:44
• You're right, I have changed the title to better reflect the problem. May 14 at 11:35