model

Predicted Incrementality by Experimentation (PIE) model.

Randomised controlled trials (RCTs) — geo experiments or ghost-ad holdouts — are considered the gold standard for measuring the incremental effect of an ad campaign. However, they are costly and slow, so advertisers only typically run them for a fraction of their campaigns. PIE turns that fraction into leverage by fitting a supervised model on the corpus of campaigns that did receive an RCT, learning the map from observable campaign features to experimentally measured incrementality, then predicts incrementality for the campaigns that never ran an experiment.

For campaign \(i\) with feature vector \(x_i\) and RCT-measured incrementality \(\tau_i\), PIE models

\[\tau_i = f(x_i) + \varepsilon_i, \quad \varepsilon_i \sim \mathrm{Normal}(0, \sigma),\]

where \(f\) is a Bayesian Additive Regression Trees (BART) ensemble — a sum of regularised regression trees. Because \(f\) is sampled rather than point-estimated, the predicted incrementality for a new campaign with features \(x_\star\) is a full posterior over \(f(x_\star)\).

The approach rests on three assumptions:

1. the RCT corpus is representative of the campaigns being predicted (predictions far outside the corpus’s feature support are extrapolation and unreliable) 2. the recorded features carry enough signal to explain variation in incrementality 3. measured incrementality is a consistent estimate of the true causal effect (per-RCT measurement error is not yet modelled — see PIEModel).

For the full method, see [1].

References

[1]

Gordon, B. R., Moakler, R., & Zettelmeyer, F. (2026). Predicted Incrementality by Experimentation (PIE) for Ad Measurement. NBER Working Paper No. 35044.

Classes

PIEModel(*[, pre_determined_features, ...])

Predicted Incrementality by Experimentation model.