IntervalGP-VAE: Learning Unobserved Confounders with Uncertainty for Personalized Causal Effect Estimation

Zhigao Guo, Feng Dong

Keywords: Causal inference, Individual treatment effect (ITE), Unobserved confounding, Proxy variables, Gaussian process, VAE.

TL;DR: This paper proposes IntervalGP-VAE, a principled variational framework that integrates interval Gaussian processes as structured priors to recover latent confounders and quantify uncertainty in individual treatment effect (ITE) estimation.

Abstract: Estimating individual treatment effects (ITEs) in the presence of unobserved confounding remains a central challenge in causal inference. Existing proxy-based methods aim to recover latent confounders from observational proxies, but typically produce only point estimates without uncertainty quantification. This lack of uncertainty modeling leads to incomplete and potentially insufficient information for downstream decision-making, especially when uncertainty is inherent in the data. We propose IntervalGP-VAE, a novel framework that combines variational autoencoders with Gaussian Process (GP) to model both the latent confounders and their associated uncertainty. At the core of our method is an interval-valued GP prior, which enables the model to capture a distribution over plausible latent confounders and treatment responses, rather than relying on potentially unreliable point estimates. This approach accounts for uncertainty arising from noisy and imperfect proxy variables and yields calibrated ITE interval to support more robust causal decisions. We provide theoretical guarantees for identifiability of the latent confounder up to a smooth monotonic transformation under weak assumptions. Experiments on synthetic and semi-synthetic datasets demonstrate that IntervalGP-VAE achieves superior performance in ITE estimation and uncertainty calibration, outperforming existing methods.

Primary Area: causal reasoning

Submission Number: 3743