Impossibility of Distribution-Free Predictive Inference for Individual Treatment Effects

TL;DR

This paper proves that distribution-free predictive inference for individual treatment effects cannot be achieved with meaningful precision under standard causal assumptions, highlighting fundamental limitations in the field.

Contribution

It establishes fundamental impossibility results showing that distribution-free prediction sets for ITEs must be trivial, revealing intrinsic limitations of current approaches.

Findings

Any distribution-free ITE prediction set with desired coverage must be infinite in expected length.

Impossibility results hold both in finite-sample and asymptotic regimes.

The analysis links ITE inference difficulty to the hardness of conditional independence testing.

Abstract

Uncertainty quantification for individual treatment effects (ITEs) is a daunting challenge in causal inference. Motivated by recent advances in conformal prediction, several works aim to construct distribution-free prediction sets for ITEs with desired coverage under standard assumptions such as strong ignorability and overlap. In this paper, we show that such goals are fundamentally unattainable in the presence of continuous covariates. Specifically, we establish finite-sample and asymptotic impossibility results demonstrating that any distribution-free prediction set achieving desired coverage for ITEs must be trivial, in the sense that it has infinite expected length. Our analysis relies on a connection between ITE inference and the hardness of conditional independence testing, and highlights the intrinsic limitations imposed by the missing data nature of causal inference. These results provide a new perspective on existing methods, clarifying that their apparent success necessarily relies on additional structural assumptions beyond standard causal assumptions.