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 provides 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 Interval Gaussian Processes (GPs) to model both the latent confounders and their associated uncertainty. This approach accounts for uncertainty arising from noisy and imperfect proxy variables and yields calibrated ITE intervals to support more robust causal decisions. We provide theoretical guarantees for identifiability of the latent confounder up to a smooth invertible reparameterisation under weak assumptions. Experiments on identifiable synthetic datasets show that IntervalGP-VAE achieves accurate ITE estimation, reliable latent recovery, and well-calibrated ITE intervals. On the semi-synthetic IHDP benchmark, IntervalGP-VAE provides competitive PEHE and ATE estimation, sharper intervals, and lower computational cost.