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Semiparametric Efficient Tests for Interpretable Distributional Treatment Effects

NeurIPS 2026 · Probabilistic and scientific modeling › Treatment effects · approach: Distributional treatment effects

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Proposes DR-ME, a doubly robust, cross-fitted finite-location kernel test for interventional distributional treatment effects, with chi-square calibration, noncentral local power, and covariance-whitened learning of test locations.

Problem

Global kernel tests detect that interventional outcome laws differ but do not show where; finite-location mean-embedding tests are invalid under observational confounding unless the feature is orthogonal to nuisance error.

Approach

Derives an orthogonal augmented inverse-propensity kernel feature at fixed outcome locations whose centered form is the canonical gradient of the finite witness; uses its covariance for a Hotelling-type statistic and learns locations by maximizing a ridge-whitened local-power criterion on a separate split.

Key results

• Under the confounded null, DR-ME stays near nominal 0.05 type-I error, while IPW-ME, DM-ME, naive observed ME and DR-ME-NoSplit over-reject.
• Among calibrated methods, DR-ME is the most powerful on localized alternatives, outperforming global DR-xKTE and random-location DR-ME-Rand.
• On non-scalar two-bump ablation (d_Y=5), full covariance whitening reaches 0.940 rejection vs 0.135 for raw witness maximization under the alternative, with null rejection near 0.05.

Surprising findings

• Naive, plug-in, and no-split variants over-reject under the null in the confounded setting, so orthogonalization and sample splitting are both needed for calibration.
• Raw witness magnitude is a poor location-learning objective; a large discrepancy in a high-variance direction can be weaker for testing than a smaller one in a low-noise direction.

Limitations

• Finite fixed location set need not characterize all global alternatives, so power is limited to alternatives visible through selected coordinates.
• Gradient-based location search certifies only stationarity, not global optimality; optimization gap must be controlled separately.
• Theory covers point treatments under observed confounding only.

Experimental setup

Datasets: MedMNIST OCTMNIST (semi-synthetic) synthetic confounded observational data

Benchmarks: synthetic confounded observational tests OCTMNIST semi-synthetic

Metrics: type-I error rejection rate / power

Baselines: DR-xKTE DR-ME-Rand IPW-ME DM-ME Naive observed ME DR-ME-NoSplit

Builds on: counterfactual mean embeddings doubly robust kernel tests (DR-xKTE) ME test feature learning Hotelling statistic

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