ArXiv

Semiparametric Efficient Test for Interpretable Distributional Treatment Effects

2026-05-08 · 17:23 UTC ·Houssam Zenati, Arthur Gretton ·1 min read

Authors: Houssam Zenati, Arthur Gretton
Categories: stat.ML, cs.LG
arXiv: https://arxiv.org/abs/2605.08034v1
PDF: https://arxiv.org/pdf/2605.08034v1

Brief

Distributional treatment effects that leave means unchanged are targeted by DR-ME, a semiparametrically efficient finite-location test (Zenati & Gretton, arXiv:2605.08034v1, 2026-05-08). From observational data it derives orthogonal doubly robust kernel features whose centered oracle is the canonical gradient; for fixed locations the test is chi-square calibrated and has noncentral chi-square local power with covariance whitening optimizing local SNR. Sample splitting preserves post-selection validity; experiments show near-nominal Type-I error and competitive power, with learned locations that localize effects in a semi-synthetic medical-imaging study.

Why it matters

DR-ME, proposed by Houssam Zenati and Arthur Gretton (arXiv 2026-05-08), is the first semiparametrically efficient finite-location test that returns interpretable causal-discrepancy coordinates for distributional treatment effects rather than only a global rejection.

Key details

The method constructs orthogonal, doubly robust kernel features from observational data whose centered oracle form is the canonical gradient of the finite witness; for fixed locations the test is chi-square calibrated under the null and has noncentral chi-square local power, employing covariance whitening that optimizes local signal-to-noise.
DR-ME uses a principled location-learning criterion with sample splitting to preserve post-selection validity; experiments report near-nominal Type-I error, competitive power versus global doubly robust kernel tests, and interpretable learned locations in a semi-synthetic medical-imaging study.

Source evidence

Abstract

Distributional treatment effects can be invisible to means: a treatment may preserve average outcomes while changing tails, modes, dispersion, or rare-event probabilities. Kernel tests can detect discrepancies between interventional outcome laws, but global tests do not reveal where the laws differ. We propose DR-ME, to our knowledge the first semiparametrically efficient finite-location test for interpretable distributional treatment effects. DR-ME evaluates an interventional kernel witness at learned outcome locations, returning causal-discrepancy coordinates rather than only a global rejection. From observational data, we derive orthogonal doubly robust kernel features whose centered oracle form is the canonical gradient of this finite witness. For fixed locations, we characterize the local testing limit: DR-ME is chi-square calibrated under the null, has noncentral chi-square local power, and uses the covariance whitening that optimizes local signal-to-noise for discrepancies visible through the selected coordinates. This efficient local-power geometry yields a principled location-learning criterion, with sample splitting preserving post-selection validity. Experiments show near-nominal type-I error, competitive power against global doubly robust kernel tests, and interpretable learned locations that localize distributional effects in a semi-synthetic medical-imaging study.