We study causal effect estimation in a setting where the data are not i.i.d.

However, it is known that even with infinite i.i.d.

We study causal effect estimation in a setting where the data are not i.i.d.$\ $(independent and identically distributed). We focus on exchangeable data satisfying an assumption of independent causal mechanisms. Traditional causal effect estimation frameworks, e.g., relying on structural causal models and do-calculus, are typically limited to i.i.d.

Just as the majority of machine learning methods, existing work focuses on studying $\textit{independent and identically distributed}$ data. However, it is known that even with infinite $i.i.d.\$ data, constraint-based methods can only identify causal structures up to broad Markov equivalence classes, posing a fundamental limitation for causal discovery. In this work, we observe that exchangeable data contains richer conditional independence structure than $i.i.d.\$ data, and show how the richer structure can be leveraged for causal discovery. We first present causal de Finetti theorems, which state that exchangeable distributions with certain non-trivial conditional independences can always be represented as $\textit{independent causal mechanism (ICM)}$ generative processes. We then present our main identifiability theorem, which shows that given data from an ICM generative process, its unique causal structure can be identified through performing conditional independence tests. We finally develop a causal discovery algorithm and demonstrate its applicability to inferring causal relationships from multi-environment data.

We present a novel model architecture which leverages deep learning tools to perform exact Bayesian inference on sets of high dimensional, complex observations. Our model is provably exchangeable, meaning that the joint distribution over observations is invariant under permutation: this property lies at the heart of Bayesian inference. The model does not require variational approximations to train, and new samples can be generated conditional on previous samples, with cost linear in the size of the conditioning set. The advantages of our architecture are demonstrated on learning tasks that require generalisation from short observed sequences while modelling sequence variability, such as conditional image generation, few-shot learning, and anomaly detection.

We present a novel model architecture which leverages deep learning tools to perform exact Bayesian inference on sets of high dimensional, complex observations.

We study causal effect estimation in a setting where the data are not i.i.d.

However, it is known that even with infinite i.i.d.

We thank the reviewers for the constructive feedback, which will significantly improve the paper. We elaborate on this first and address specific comments and questions from the reviewers below. RWS, etc.) applications assumes the data is generated iid and and achieve scalability through use of subsampling and The current discussion in Section 3.5 for MSC on the other hand focuses on the more challenging case, We will clarify this in the revision. We compare the base versions of the respective algorithms. We will add these references to the related work section.

We study causal effect estimation in a setting where the data are not i.i.d. We focus on exchangeable data satisfying an assumption of independent causal mechanisms. Traditional causal effect estimation frameworks, e.g., relying on structural causal models and do-calculus, are typically limited to i.i.d. To address this gap, we develop a generalized framework for exchangeable data and introduce a truncated factorization formula that facilitates both the identification and estimation of causal effects in our setting. To illustrate potential applications, we introduce a causal Pólya urn model and demonstrate how intervention propagates effects in exchangeable data settings.