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Impossibility of Distribution-Free Predictive Inference for Individual Treatment Effects

NeurIPS 2026 · Probabilistic and scientific modeling › Treatment effects · approach: Distributional treatment effects · 0 citations (OpenAlex)

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Shows that distribution-free valid prediction sets for individual treatment effects under strong ignorability and overlap must be trivial (infinite expected length) when covariates are continuous, and proposes a Split-Pair interval that is valid under an additive model with residual independence assumptions.

Problem

Whether distribution-free predictive inference (valid coverage with informative, finite-length sets) for individual treatment effects is possible under standard causal assumptions (strong ignorability, overlap) with continuous covariates.

Approach

Connects ITE predictive inference to hardness of conditional independence testing with continuous conditioning variables: any uniformly valid ITE prediction set yields a valid test, forcing it to cover every real value and have infinite expected length. Also gives a positive Split-Pair procedure under additive-error and residual-independence assumptions.

Key results

• Split-Pair attains the nominal 0.9 coverage across all four scenarios in the independent-error beta-propensity setting, while Nest-Exact is highly conservative.
• With Corr(eps0, eps1) = -0.5, Split-Pair fails to reach the 0.9 target, as expected since its independence assumption is violated.
• In the checkerboard stress test, all methods, including Naive and Nest-Exact, fall below the identity line in realized coverage.

Surprising findings

• Conservative methods such as Naive and Nest-Exact fail to attain nominal coverage in the checkerboard stress-test design.
• Nest-Inexact fails to reach target coverage even in the simple example with uninformative covariates, with coverage about 0.755 against a 0.9 target.

Limitations

• Positive Split-Pair result requires restrictive additive model with residuals independent of covariates and conditional independence of potential outcomes, which fails under negative correlation.
• Impossibility argument depends on continuous covariates; discrete or no-covariate settings are left open.

Experimental setup

Benchmarks: synthetic simulation designs

Metrics: empirical coverage average interval length

Baselines: Naive Bonferroni Nest-Exact Nest-Inexact DR pseudo-interval IPW

Builds on: conformal prediction Lei and Candès 2021 conformal inference for counterfactuals Alaa et al. 2023 conformal meta-learners Shah and Peters conditional independence testing hardness

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