Using Causal Trees

Should always be thinking in this direction.   Usefully integrating analysis and reality with process.

Understanding Causal Trees       Towards Data Science by Matteo Courthoud / February 03, 2023  

How to use regression trees to estimate heterogeneous treatment effects.

In causal inference, we are usually interested in estimating the causal effect of a treatment (a drug, ad, product, …) on an outcome of interest (a disease, firm revenue, customer satisfaction, …). However, knowing that a treatment works on average is often not sufficient and we would like to know for which subjects (patients, users, customers, …) it works better or worse, i.e. we would like to estimate heterogeneous treatment effects.

Estimating heterogeneous treatment effects allows us to use the treatment selectively and more efficiently through targeting. Knowing which customers are more likely to react to a discount allows a company to spend less money by offering fewer but better-targeted discounts. This works also for negative effects: knowing for which patients a certain drug has side effects allows a pharmaceutical company to warn or exclude them from the treatment. There is also a more subtle advantage of estimating heterogeneous treatment effects: knowing for whom a treatment works allow us to better understand how a treatment works. Knowing that the effect of a discount does not depend on the income of its recipient but rather on its buying habits tells us that maybe it is not a matter of money, but rather a matter of attention or loyalty.

In this article, we will explore the estimation of heterogeneous treatment effects using a modified version of regression trees (and forests). From a machine-learning perspective, there are two fundamental differences between causal trees and predictive trees. First of all, the target is the treatment effect, which is an inherently unobservable object. Second, we are interested in doing inference, which means quantifying the uncertainty of our estimates.

Online Discounts and Targeting

For the rest of the article, we are going to use a toy example, for the sake of exposition: suppose we were an online shop and we are interested in understanding whether offering discounts to new customers increases their expenditure. In particular, we would like to know if offering discounts is more effective for some customers with respect to others since we would prefer not to give discounts to customers that would spend anyways. Moreover, it could also be that spamming customers with pop-ups could deter them from buying, having the opposite effect.  ... '