# Interventional Processes for Causal Uncertainty Quantification

arXiv: https://arxiv.org/abs/2410.14483 · HTML: https://mlsanity.com/paper/2410.14483/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 56 references that are in the map.
- First posted on arXiv 18 Oct 2024.

## Builds on (most cited first, 28 of 28)

- [Accurate Uncertainties for Deep Learning Using Calibrated Regression](https://mlsanity.com/paper/1807.00263/) (2018)
- [Gaussian Processes and Kernel Methods: A Review on Connections and Equivalences](https://mlsanity.com/paper/1807.02582/) (2018)
- [A General Framework for Updating Belief Distributions](https://mlsanity.com/paper/1306.6430/) (2013)
- [Bayesian Inference of Individualized Treatment Effects using Multi-task Gaussian Processes](https://mlsanity.com/paper/1704.02801/) (2017)
- [Semiparametric doubly robust targeted double machine learning: a review](https://mlsanity.com/paper/2203.06469/) (2022)
- [Sobolev Norm Learning Rates for Regularized Least-Squares Algorithm](https://mlsanity.com/paper/1702.07254/) (2017)
- [A Measure-Theoretic Approach to Kernel Conditional Mean Embeddings](https://mlsanity.com/paper/2002.03689/) (2020)
- [Discussion on "Bayesian Regression Tree Models for Causal Inference: Regularization, Confounding, and Heterogeneous Effects" by Hahn, Murray and Carvalho](https://mlsanity.com/paper/2108.02836/) (2021)
- [Nonparametric methods for doubly robust estimation of continuous treatment effects](https://mlsanity.com/paper/1507.00747/) (2015)
- [Robust Generalised Bayesian Inference for Intractable Likelihoods](https://mlsanity.com/paper/2104.07359/) (2021)
- [Orthogonal Random Forest for Causal Inference](https://mlsanity.com/paper/1806.03467/) (2018)
- [Causal Bayesian Optimization](https://mlsanity.com/paper/2005.11741/) (2020)
- [Kernel Methods for Causal Functions: Dose, Heterogeneous, and Incremental Response Curves](https://mlsanity.com/paper/2010.04855/) (2020)
- [General Bayesian Updating and the Loss-Likelihood Bootstrap](https://mlsanity.com/paper/1709.07616/) (2017)
- [Calibrating general posterior credible regions](https://mlsanity.com/paper/1509.00922/) (2015)
- [Deconditional Downscaling with Gaussian Processes](https://mlsanity.com/paper/2105.12909/) (2021)
- [DoubleML -- An Object-Oriented Implementation of Double Machine Learning in Python](https://mlsanity.com/paper/2104.03220/) (2021)
- [Towards Optimal Sobolev Norm Rates for the Vector-Valued Regularized Least-Squares Algorithm](https://mlsanity.com/paper/2312.07186/) (2023)
- [BayesIMP: Uncertainty Quantification for Causal Data Fusion](https://mlsanity.com/paper/2106.03477/) (2021)
- [Bayesian Learning of Kernel Embeddings](https://mlsanity.com/paper/1603.02160/) (2016)
- [Calibrating Deep Convolutional Gaussian Processes](https://mlsanity.com/paper/1805.10522/) (2018)
- [Causal Inference using Gaussian Processes with Structured Latent Confounders](https://mlsanity.com/paper/2007.07127/) (2020)
- [Fast and Scalable Spike and Slab Variable Selection in High-Dimensional Gaussian Processes](https://mlsanity.com/paper/2111.04558/) (2021)
- [Scalable Cross Validation Losses for Gaussian Process Models](https://mlsanity.com/paper/2105.11535/) (2021)
- [Counterfactual Cocycles: A Framework for Robust and Coherent Counterfactual Transports](https://mlsanity.com/paper/2405.13844/) (2024)
- [Sharp Calibrated Gaussian Processes](https://mlsanity.com/paper/2302.11961/) (2023)
- [A Practical Introduction to Bayesian Estimation of Causal Effects: Parametric and Nonparametric Approaches](https://mlsanity.com/paper/2004.07375/) (2020)
- [Asymptotics of the Empirical Bootstrap Method Beyond Asymptotic Normality](https://mlsanity.com/paper/2011.11248/) (2020)

## Built on by (most cited first, 2 of 2)

- [Kernel-based estimators for functional causal effects](https://mlsanity.com/paper/2503.05024/) (2025)
- [ActiveCQ: Active Estimation of Causal Quantities](https://mlsanity.com/paper/2509.24293/) (2025)

## Abstract (arXiv)

Reliable uncertainty quantification for causal effects is crucial in high-stakes applications, but remains challenging when the target is an entire function rather than a scalar estimand. In this work, we introduce a GP-based approach for uncertainty quantification of interventional functions. The central idea is to build on recent work representing interventional functions as an inner-product of observational functions in a reproducing kernel Hilbert space (RKHS), by constructing appropriate GP priors for such functions and inferring posteriors from observational data. Our approach yields closed-form posterior moments and tractable training and inference, while avoiding pathologies of previous GP prior constructions for RKHS functions. We further derive a practical procedure for posterior coverage calibration. Across synthetic benchmarks, causal Bayesian optimization tasks, and a large-scale real dataset, our method improves uncertainty quantification while remaining competitive in causal effect estimation.