Reliable Selection of Heterogeneous Treatment Effect Estimators

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 $\text{EMSE}_τ$ 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, Hillstrom and Starbucks uplift datasets we match Qini coefficient performance of S-, T-learner and GRF baselines. An open-source Python package with reproducible seeds, sklearn-compatible API, and full test coverage accompanies this work (https://codeberg.org/hadjipantelis/rattus).

A central goal of modern causal inference is estimating heterogeneous treatment effects to answer questions like "how does an intervention affect each unit," rather than only on average. We study this problem with panel-data where we observe $n$ units across $m$ times under unknown, non-uniform treatment assignments. The data in this setting is naturally represented as a matrix of all unit--time treatment effects. Estimating heterogeneous treatment effects can then be expressed as obtaining a good estimation of each row's average in this matrix. This allows us to formulate the problem as matrix completion, which can be solved under natural low-rankness assumptions. However, existing matrix-completion guarantees are not powerful enough to get meaningful bounds for the per-row guarantee required for estimating the heterogeneous treatment effect; roughly speaking, they are only useful for estimating average treatment effect bounds, as also illustrated in a recent line of work. We give a simple, computationally efficient estimator that, without knowledge of the propensities and under standard low-rankness and regularity assumptions, achieves a row-wise $\ell_2$ error of $\tilde{O}(\sqrt{\frac{1}{n} + \frac{n}{m^2}})$. Technically, our analysis establishes the first sharp row-wise $\ell_2$-perturbation bound for low-rank approximation, complementing existing spectral-, Frobenius-, and entrywise perturbation theory.

In selective deployment, practitioners act only on a model-chosen subset of individuals based on predicted conditional average treatment effects, but marginal conformal guarantees need not control reliability on that selected subset. We study reliable selection for black-box CATE predictors: selecting candidates whose CATE errors are below a tolerance while controlling the false discovery rate (FDR). Since CATE errors are unobservable, we construct doubly robust proxy errors from pseudo-outcomes; however, naive proxies can lose power under heteroskedasticity because variance overwhelms the reliability signal. We propose Denoised Conformal Alignment, which subtracts an estimated conditional variance component and combines conformal calibration with Benjamini--Hochberg selection. Our analysis shows that validity is governed by stability of proxy/oracle threshold labels, rather than pointwise perfection of the variance estimator. Experiments show substantially improved power while maintaining FDR control across challenging settings.