Heterogeneous Treatment Effects (CATE)

By the end of this lesson, you should be able to: say what a CATE is and how it differs from the average effect, build S, T and X learners and explain what each one's structure does to the answer, validate an effect model without ever observing an individual effect, and judge whether a targeting rule is worth more than shipping to everyone.

The average is not the decision

Alder Ads piloted a new automated bidding tool on a random half of 60,000 advertisers. The readout is clean, because the pilot was randomised and nothing from modules 2 through 5 is needed here.

Ship it. Except the average is hiding the shape of the thing.

The tool automates bidding decisions, so it's worth a lot to an advertiser still working by hand across many campaigns and less than nothing to one that already automated. Ship to everyone and you are knowingly making a quarter of your advertisers worse off to capture the average.

The conditional average treatment effect is what you'd need to avoid that: not one number but a function, $\tau(X) = E[Y(1) - Y(0) \mid X]$, an effect per advertiser given what you know about them.

Three ways to build one

Every metalearner is a recipe for turning ordinary prediction models into an effect model.1

S-learner. One model with treatment as a feature. Predict each advertiser twice, flag on and flag off, and difference.

T-learner. Two models, one per arm. Predict with both and difference.

X-learner. Use each arm's model to impute the other arm's missing counterfactual, then fit a model to those imputed effects and blend the two by the propensity.

Same gradient boosting configuration for all three, so what follows is about the recipes rather than the hyperparameters.

All three get the average about right, which is the easy part. They disagree substantially about who it's for.