Venue: ICLR 2023 Conference

Reviews:

final_score: rating: 8: accept, good paper
review_content: summary_of_the_paper: Basically, this paper aims to study the problem of evaluating the counterfactual statements based on neural models. To achieve this goal, the authors firstly detail the previous work on the causal neural models, and then propose to identify counterfactual quantities based on the first two causal layers. The authors have also proved the soundness and completeness, which makes the paper very solid. 

strength_and_weaknesses: In general, the paper is well-written, and it aims to solve an important and interesting problem. The experiment can support the claims in the paper, and the authors have provided a very detailed appendix, which can help to understand their ideas.
I do not find significant weaknesses in this paper. 
clarity,_quality,_novelty_and_reproducibility: The paper is novel and the proposed solution is sound.
summary_of_the_review: see the above comments
review_title: null

final_score: rating: 8: accept, good paper
review_content: summary_of_the_paper: This paper builds the basic theoretical result for neural counterfactual inference. Based on the theoretical results, the authors present the algorithm to determine the identification of counterfacual and give the algorithm to estimate it if it is identifiable.
strength_and_weaknesses: Strength:
1. Counterfactual inference is an interesting topic. This paper takes deep learning techniques into counterfactual inference, which could inspire more related studies.

2. The paper presents solid theoretical results.

Weaknesses:
The paper is hard to read. I understand that there are many new results, but it will be better if the authors could clearly illustrate the value of their theoretical results and the challenge. 
clarity,_quality,_novelty_and_reproducibility: As far as I understand, the main contribution is on theory. I suggest the authors emphasize what the challenge is for their main result. For example, for me, Thm. 1 seems to be an evident result, because the neural causal model is just to use many feedforward neural networks to model each causal mechanism P(V_i|pa(V_i)) according to my understanding of Def. 2. Could the authors give some intuition about why it is not evident, or does I miss or misunderstand some important facts?

My other questions:
1. Could the authors explain "It may be concerning that the true SCM $M^*$ might not be an NCM, as we alluded to earlier." further? Where does it allude?
2. How to determine Line 4 of Alg. 1?
3. Under the current framework, does the proposed algorithm only apply when the data is discrete?
summary_of_the_review: After the rebuttal, I increase my score.

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Currently, I can only give a baseline score because I am not sure about the studies in this paper. I look forward to the response of the authors.
review_title: null

final_score: rating: 6: marginally above the acceptance threshold
review_content: summary_of_the_paper: This paper advances the theory of neural causal models and prove that they can recover the counterfactuals (L3 in Pearl's ladder of causality). The authors also provide new identification results and Algorithm 1 that uses supervised learning techniques to tell if the causal prior constraints are sufficient for identification. Finally, they propose GAN-NCM to scale causal models to high dimensional data.
strength_and_weaknesses: The overall arguments of the paper seem intuitive and correct. Although, the authors do not provide short overview of the proofs and the paper looks a bit jammed (better fits a journal paper). The paper heavily relies on the familiarity of the audience with the recent prior works such as (Bareinboim et al., 2022). Thus, some of the statements of the paper are unclear and need more explanations. E.g., "Our treatment is constrained to recursive SCMs, which implies acyclic causal diagrams, with finite domains over V."
The use of the term neural seems to be mostly for marketing purposes and the results of the paper may hold for general function estimators. 

clarity,_quality,_novelty_and_reproducibility: The authors have jammed tons of materials within the page limit and this has severely decreased readability of the paper. The results of the paper are novel for a conference publication. The experimental section is not extensive and reproducibility is not a key issue for this paper.
summary_of_the_review: This paper advances the theory of neural causal models and prove that they can recover the counterfactuals (L3 in Pearl's ladder of causality). The authors also provide new identification results and Algorithm 1 that uses supervised learning techniques to tell if the causal prior constraints are sufficient for identification. Finally, they propose GAN-NCM to scale causal models to high dimensional data.
review_title: null

Meta-review: metareview:_summary,_strengths_and_weaknesses: The paper introduces new algorithms for estimating counterfactual quantities, such as as natural direct effects. In particular, identifiability is not necessary, and as such it extends the scope of causal inference to many problems of interest where knowledge provided is still informative even if it does not imply a unique answer.

Strengths: it tackles a broad class of problems of central importance in causal inference while being nicely written and of practical relevance, and easy to use in principle.

Weaknesses: overlap with other existing work, like Xia et al., removes some of the impact (but there are more than enough new ideas here). I would also recommend citing Hu, Y., Wu, Y., Zhang, L., and Wu, X. (2021). A generative adversarial framework for bounding confounded causal effects, AAAI, which covers some similar ground.
justification_for_why_not_higher_score: Overlap with other existing work, like Xia et al., removes some of the impact (but there are more than enough new ideas here). 
justification_for_why_not_lower_score: It tackles a broad class of problems of central importance in causal inference while being nicely written and of practical relevance, and easy to use in principle.
Decision: Accept: poster