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We formulate a general framework for building structural causal models (SCMs) with deep learning components. The proposed approach employs normalising flows and variational inference to enable tractable inference of exogenous noise variables - a crucial step for counterfactual inference that is missing from existing deep causal learning methods. Our framework is validated on a synthetic dataset built on MNIST as well as on a real-world medical dataset of brain MRI scans. Our experimental results indicate that we can successfully train deep SCMs that are capable of all three levels of Pearl's ladder of causation: association, intervention, and counterfactuals, giving rise to a powerful new approach for answering causal questions in imaging applications and beyond.

POST REBUTTAL -- I have read the authors' responses and other reviewers' comments. Unfortunately, some of my primary concerns have not been addressed, which I will elaborate on below. This paper studies the implementation of Pearl's in a SCM, where each of its functions is represented as a neural network. The authors claim that the proposed approaches "are capable of all three levels of Pearl's ladder of causation: association, intervention, and counterfactuals giving rise to a powerful new approach for answering causal questions in imaging applications and beyond." However, I believe the significance of its contributions to the causal inference literature is a bit overstated. In particular, the authors assume that detailed parameterization of the target SCM is *precisely known*.

The reviewers agree on the whole that this work addresses an important problem and that the paper makes sound, well-supported claims. The rebuttal did a good job at clarifying the scope of their work, largely improving the scores of the reviewers. I urge the authors to carefully update the paper to address the reviewers concerns in the final version. Examples of what to improve include: - Description of the "intervention vs counterfactual" distinction. One reviewer recommends: "since it is key for the paper's novelty claim I think this distinction needs a little more explanation, perhaps through a simple example" - Engage with the existing literature on causal inference.

We formulate a general framework for building structural causal models (SCMs) with deep learning components. The proposed approach employs normalising flows and variational inference to enable tractable inference of exogenous noise variables - a crucial step for counterfactual inference that is missing from existing deep causal learning methods. Our framework is validated on a synthetic dataset built on MNIST as well as on a real-world medical dataset of brain MRI scans. Our experimental results indicate that we can successfully train deep SCMs that are capable of all three levels of Pearl's ladder of causation: association, intervention, and counterfactuals, giving rise to a powerful new approach for answering causal questions in imaging applications and beyond.

Abstract: We formulate a general framework for building structural causal models (SCMs) with deep learning components. The proposed approach employs normalising flows and variational inference to enable tractable inference of exogenous noise variables - a crucial step for counterfactual inference that is missing from existing deep causal learning methods. Our framework is validated on a synthetic dataset built on MNIST as well as on a real-world medical dataset of brain MRI scans. Our experimental results indicate that we can successfully train deep SCMs that are capable of all three levels of Pearl's ladder of causation: association, intervention, and counterfactuals, giving rise to a powerful new approach for answering causal questions in imaging applications and beyond. The code for all our experiments is available at this https URL.