# Addressing Positivity Violations in Causal Effect Estimation using Gaussian Process Priors

arXiv: https://arxiv.org/abs/2110.10266 · HTML: https://mlsanity.com/paper/2110.10266/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Oct 2021.

## Built on by (most cited first, 3 of 3)

- [Eliciting Numerical Predictive Distributions of LLMs Without Autoregression](https://mlsanity.com/paper/2603.02913/) (2026)
- [Local Gaussian process extrapolation for BART models with applications to causal inference](https://mlsanity.com/paper/2204.10963/) (2022)
- [A flexible Bayesian g-formula for causal survival analyses with time-dependent confounding](https://mlsanity.com/paper/2402.02306/) (2024)

## Abstract (arXiv)

In observational studies, causal inference relies on several key identifying assumptions. One identifiability condition is the positivity assumption, which requires the probability of treatment be bounded away from 0 and 1. That is, for every covariate combination, it should be possible to observe both treated and control subjects, i.e., the covariate distributions should overlap between treatment arms. If the positivity assumption is violated, population-level causal inference necessarily involves some extrapolation. Ideally, a greater amount of uncertainty about the causal effect estimate should be reflected in such situations. With that goal in mind, we construct a Gaussian process model for estimating treatment effects in the presence of practical violations of positivity. Advantages of our method include minimal distributional assumptions, a cohesive model for estimating treatment effects, and more uncertainty associated with areas in the covariate space where there is less overlap. We assess the performance of our approach with respect to bias and efficiency using simulation studies. The method is then applied to a study of critically ill female patients to examine the effect of undergoing right heart catheterization.