๐ค AI Summary
Existing methods for heterogeneous treatment effect estimation often struggle to simultaneously ensure sensitivity in detecting effect modifiers and validity in statistical inference. This work proposes a hybrid algorithm that integrates significance-driven splitting with honest estimation: it employs the tยฒ statistic as the splitting criterion, incorporates honest sample splitting, selects the cost-complexity penalty via cross-validation, and uses the infinitesimal jackknife to estimate Monte Carlo variance. This approach is the first to align significance-based splitting with an honest estimation framework, maintaining theoretical consistency under strong interactions and providing nominal leaf-level confidence intervals for a single tree. Empirical results demonstrate approximately 90% coverage (nominal 90%) on AtheyโImbens synthetic data and Qini coefficients on par with S- and T-learners on real-world Criteo and Starbucks datasets.
๐ Abstract
Estimating heterogeneous treatment effects (CATE) requires simultaneously detecting effect modification and quantifying estimation uncertainty. Existing tree-based methods make an uneasy trade-off: significance-based approaches (Radcliffe and Surry 2011) identify subgroup interactions directly but lack valid inference; honest causal trees (Athey and Imbens 2016) deliver nominal confidence interval coverage but use outcome-agnostic splitting criteria that sacrifice interaction sensitivity. We introduce a hybrid algorithm that fuses significance-based splitting with honest sample-splitting and cross-validation. Our splitting criterion uses the squared $t$-statistic for the treatment $\times$ side interaction ($t^2$), which is shown to be directly aligned with the honest $\text{EMSE}_ฯ$ criterion when the interaction is strong. Post-hoc honest cross-validation selects the cost-complexity penalty, giving a single principled estimator with nominal CI coverage at the leaf level. For forests, we retain bootstrap count vectors to enable an infinitesimal jackknife (IJ) variance estimate of Monte-Carlo convergence rather than formal pointwise inference. On the three synthetic designs from (Athey and Imbens 2016) the single tree achieves approximately 90\% leaf-average CI coverage at the 90\% nominal level across all three designs (200 replications each); on the Criteo and Starbucks uplift datasets we match Qini coefficient performance of S- and T-learner baselines. An open-source Python package with reproducible seeds, sklearn-compatible API, and full test coverage accompanies this work (https://codeberg.org/hadjipantelis/rattus).