Practice — Uplift Modeling & Heterogeneous Treatment Effects (6 questions)

A streaming service wants to send a retention offer (three months at a reduced price) to subscribers who are about to hit their renewal date. A past randomized test shows these segments among 8,000 at-risk subscribers. The offer costs $8 per subscriber who receives it (contact plus discount budget, paid whether or not they stay) and a retained subscriber is worth $60 of future margin.

1. Name each segment's quadrant and compute its uplift \tau.
2. Compute the average treatment effect over the 8,000 subscribers and the profit of sending the offer to everyone.
3. The team has a model of "probability to retain given the offer" and can afford 1,000 offers. Compute the incremental retained subscribers and profit of targeting by that model versus by uplift.
4. A product manager says "B is our best audience, they respond to everything". Rebut this in two sentences.

A growth team ran a push-notification test on 400,000 users. For operational reasons only 2 percent (8,000 users) received the push and 98 percent served as control; assignment was random with a known propensity of 0.02. Baseline 7-day activity is about 10 percent. They want to rank users by incremental activity and push the top 30 percent.

1. Explain what goes wrong with a naive S-learner and with a plain T-learner here.
2. Describe the X-learner steps and why the propensity enters the final blend. Which part of the model uses the large control group?
3. The team asks "which learner should we ship?". Recommend an approach, including the final-stage model, a second alternative to compare against and the validation metric.
4. How noisy will an uplift@30% measurement on a held-out slice be? Compute its standard error assuming the test slice keeps the 2/98 split and 10 percent activity in both arms.