# Multi-task Causal Learning with Gaussian Processes

arXiv: https://arxiv.org/abs/2009.12821 · HTML: https://mlsanity.com/paper/2009.12821/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Sep 2020.

## Built on by (most cited first, 14 of 14)

- [Causal Machine Learning for Healthcare and Precision Medicine](https://mlsanity.com/paper/2205.11402/) (2022)
- [Model-based Causal Bayesian Optimization](https://mlsanity.com/paper/2211.10257/) (2022)
- [BayesIMP: Uncertainty Quantification for Causal Data Fusion](https://mlsanity.com/paper/2106.03477/) (2021)
- [An Adaptive Kernel Approach to Federated Learning of Heterogeneous Causal Effects](https://mlsanity.com/paper/2301.00346/) (2023)
- [Dynamic Causal Bayesian Optimization](https://mlsanity.com/paper/2110.13891/) (2021)
- [Causal Entropy Optimization](https://mlsanity.com/paper/2208.10981/) (2022)
- [Causally Abstracted Multi-armed Bandits](https://mlsanity.com/paper/2404.17493/) (2024)
- [Transfer Learning for Individual Treatment Effect Estimation](https://mlsanity.com/paper/2210.00380/) (2022)
- [Contextual Causal Bayesian Optimisation](https://mlsanity.com/paper/2301.12412/) (2023)
- [Adaptive Multi-Source Causal Inference](https://mlsanity.com/paper/2105.14877/) (2021)
- [Improve in-situ life prediction and classification performance by capturing both the present state and evolution rate of battery aging](https://mlsanity.com/paper/2308.13996/) (2023)
- [Idiographic Personality Gaussian Process for Psychological Assessment](https://mlsanity.com/paper/2407.04970/) (2024)
- [Online Identification of IT Systems through Active Causal Learning](https://mlsanity.com/paper/2509.02130/) (2025)
- [Advantages and limitations in the use of transfer learning for individual treatment effects in causal machine learning](https://mlsanity.com/paper/2512.16489/) (2025)

## Abstract (arXiv)

This paper studies the problem of learning the correlation structure of a set of intervention functions defined on the directed acyclic graph (DAG) of a causal model. This is useful when we are interested in jointly learning the causal effects of interventions on different subsets of variables in a DAG, which is common in field such as healthcare or operations research. We propose the first multi-task causal Gaussian process (GP) model, which we call DAG-GP, that allows for information sharing across continuous interventions and across experiments on different variables. DAG-GP accommodates different assumptions in terms of data availability and captures the correlation between functions lying in input spaces of different dimensionality via a well-defined integral operator. We give theoretical results detailing when and how the DAG-GP model can be formulated depending on the DAG. We test both the quality of its predictions and its calibrated uncertainties. Compared to single-task models, DAG-GP achieves the best fitting performance in a variety of real and synthetic settings. In addition, it helps to select optimal interventions faster than competing approaches when used within sequential decision making frameworks, like active learning or Bayesian optimization.