While causal models are becoming one of the mainstays of machine learning, the problem of uncertainty quantification in causal inference remains challenging. In this paper, we study the causal data fusion problem, where data arising from multiple causal graphs are combined to estimate the average treatment effect of a target variable. As data arises from multiple sources and can vary in quality and sample size, principled uncertainty quantification becomes essential. To that end, we introduce \emph{Bayesian Causal Mean Processes}, the framework which combines ideas from probabilistic integration and kernel mean embeddings to represent interventional distributions in the reproducing kernel Hilbert space, while taking into account the uncertainty within each causal graph. To demonstrate the informativeness of our uncertainty estimation, we apply our method to the Causal Bayesian Optimisation task and show improvements over state-of-the-art methods.

While causal models are becoming one of the mainstays of machine learning, the problem of uncertainty quantification in causal inference remains challenging. In this paper, we study the causal data fusion problem, where data arising from multiple causal graphs are combined to estimate the average treatment effect of a target variable. As data arises from multiple sources and can vary in quality and sample size, principled uncertainty quantification becomes essential. To that end, we introduce \emph{Bayesian Causal Mean Processes}, the framework which combines ideas from probabilistic integration and kernel mean embeddings to represent interventional distributions in the reproducing kernel Hilbert space, while taking into account the uncertainty within each causal graph. To demonstrate the informativeness of our uncertainty estimation, we apply our method to the Causal Bayesian Optimisation task and show improvements over state-of-the-art methods.

While causal models are becoming one of the mainstays of machine learning, the problem of uncertainty quantification in causal inference remains challenging. In this paper, we study the causal data fusion problem, where data arising from multiple causal graphs are combined to estimate the average treatment effect of a target variable. As data arises from multiple sources and can vary in quality and sample size, principled uncertainty quantification becomes essential. To that end, we introduce \emph{Bayesian Causal Mean Processes}, the framework which combines ideas from probabilistic integration and kernel mean embeddings to represent interventional distributions in the reproducing kernel Hilbert space, while taking into account the uncertainty within each causal graph. To demonstrate the informativeness of our uncertainty estimation, we apply our method to the Causal Bayesian Optimisation task and show improvements over state-of-the-art methods.

In the era of big data, the explosive growth of multi-source heterogeneous data offers many exciting challenges and opportunities for improving the inference of conditional average treatment effects. In this paper, we investigate homogeneous and heterogeneous causal data fusion problems under a general setting that allows for the presence of source-specific covariates. We provide a direct learning framework for integrating multi-source data that separates the treatment effect from other nuisance functions, and achieves double robustness against certain misspecification. To improve estimation precision and stability, we propose a causal information-aware weighting function motivated by theoretical insights from the semiparametric efficiency theory; it assigns larger weights to samples containing more causal information with high interpretability. We introduce a two-step algorithm, the weighted multi-source direct learner, based on constructing a pseudo-outcome and regressing it on covariates under a weighted least square criterion; it offers us a powerful tool for causal data fusion, enjoying the advantages of easy implementation, double robustness and model flexibility. In simulation studies, we demonstrate the effectiveness of our proposed methods in both homogeneous and heterogeneous causal data fusion scenarios.