Venue: ICLR 2023 Conference

Reviews:

final_score: rating: 6: marginally above the acceptance threshold
review_content: summary_of_the_paper: The paper is trying to deal with non-linear relationships in time series data and proposes a structural equation model called Rhino, which combines vector auto-regression, deep learning as well as variational inference techniques.
strength_and_weaknesses: Strength
1. The problem causal discovery the paper is trying to tackle is quite important and interesting.
2. The method is supported by the structural identifiability theory. 

Weakness
1. I do not understand why related works is not Section 2, why Section 5. This is quite confusing.
2. In the experiments section, I was wondering if we should only use AUC as the evaluation metrics since one major goal seems to be discover the causal relationships.
clarity,_quality,_novelty_and_reproducibility: The work's quality needs some improvement but the novelty of the paper is good.
summary_of_the_review: Overall, I think the paper is of good quality, with some improvements required on the experiments and writing. But the overall the methodology and theory part is good.
review_title: null

final_score: rating: 6: marginally above the acceptance threshold
review_content: summary_of_the_paper: In this paper, the authors investigate the problem of temporal causal discovery. Existing work relies on the absence of instantaneous effects with fixed noise distributions, whereas constraint-based methods require stronger faithfulness assumptions. To alleviate this problem, the authors propose Rhino, which combines vector auto-regression and deep learning, and is trained by variational inference. They further demonstrate that Rhino is structurally identifiable under similar assumptions to ANMs. Experiments are conducted on two discovery benchmarks.

strength_and_weaknesses: Strength: 
1. The authors propose to combine autoregression and deep learning, and train the network using variational inference.
2. The authors demonstrate that the proposed Rhino is structurally identifiable under similar assumptions to ANMs.
3. The paper is well written. 
 

clarity,_quality,_novelty_and_reproducibility: The paper is well written. The proposed method is novel. 
summary_of_the_review: The paper is well written. The proposed method is novel.
review_title: null

final_score: rating: 8: accept, good paper
review_content: summary_of_the_paper: This paper provides a new structure identifiability result for temporal causal discovery, specifically time-series structural equation model with nonlinear lagged and instantaneous effects. The key advancement is that the identifiability result allows for history-dependent noise, while existing works typically assume independent noise. The paper further proposes a structure identification method based on continuous optimization, variational inference, and deep learning. Empirical results for synthetic and real world data are further reported.
strength_and_weaknesses: Strengths
- The identifiability result and identification method both seem to be sound.
- Theoretical and empirical results are provided.
- The motivation of using history-dependent noise is convincing as far as I know.

Weaknesses/Main Points
- Several proof techniques are adapted from prior works. It would be clearer to explicitly acknowledge/summarize in the main paper (Section 4.1) if any of the important proof technique are adapted from prior works, instead of only mentioning in the Appendix.
- Some of the writing may be confusing. Is Rhino a type of structural equation model (SEM), or a structural identification method? In Section 3.1 and Theorem 1, it seems that Rhino is defined as a certain type of structural equation model Eq. (5). However, in Section 3.2 and many other parts, it seems that Rhino is a structure identification method that refers to Eq. (10). I think it would be clearer to make a distinction between SEM/identifiability and identification. E.g., we often use LINGAM to refer to the specific structural equation model, and ICA-LINGAM/Direct-LINGAM to refer to the specific method.
- Section 3.2 mentions that augmented Lagrangian training is used to make sure Rhino only produces DAGs. Does Theorem 2 require the augmented Lagrangian training or the DAG assumption of Rhino's solution?
    - If yes:
        - The authors should make this clear in the theorem statement. The current statement seems like any value of $\rho$ and $\alpha$ suffices, and the solution (or search space) need not be DAG.
        - Is there any theoretical guarantee that Rhino only produces DAGs with such training? What assumptions are needed? Such assumptions should also be clearly stated in the theorem statement. 
    - If no:
        - Why do we still need such DAG penalty and augmented Lagrangian training?
- What values of $\lambda$ in Eq. (10) is needed for Theorem 2 to hold? For infinite data, do we still need sparseness prior? (In many statistics/ML settings, sparseness is often used for finite samples.)
- Theorem 2: What does it specifically mean to be no model misspeficiation? Could the authors provide a precise technical definition?
- The paper should make it very clear that Theorem 2 is based on global solution of Eq. (10). In practice, it is impossible and we often end up with a local solution.
clarity,_quality,_novelty_and_reproducibility: The contributions over prior works are clear. The paper is well written. The discussion of related work is adequate. Some part of the clarity can be improved, as stated above.
summary_of_the_review: The setting considered with history-dependent noise is well-motivated. Theoretical results are provided to justify the proposed method. However, there are some concerns with Theorem 2.
review_title: null

final_score: rating: 8: accept, good paper
review_content: summary_of_the_paper: The author proposed a new structural equation model, named Rhino, that can be used to model causal relations between variables in temporal data. Compared to ANM, the proposed model is more flexible, but there is no sacrificing in identifiable properties. The proposed Rhino model is actually identifiable under some common assumptions. The experiments show that the proposed approach can be applied in various different applications to produce satisfactory results. 
strength_and_weaknesses: Strength:

1. The motivation of the paper is clearly stated, and the writing of the paper is good. It is easy to follow. Even for the hardest proof part, the sketch of the proof is easy to follow.

2. The experiment part is solid. The experiments are based on datasets from different domains, and all of them show the effectiveness of the proposed model.

3. The mathematic derivation of the paper is solid.
clarity,_quality,_novelty_and_reproducibility: This is a well written paper with enough novelty. It should be reproducible. 
summary_of_the_review: The authors proposed a new SEM, named Rhino, for temporal data, and proved the identifiable of the proposed model. Experiments on data from different domains show the effectiveness of the proposed model.
review_title: null

Meta-review: metareview:_summary,_strengths_and_weaknesses: The paper proposes a time-series structural equation model with non-linear lagged and instantaneous effects for a new structure identifiability result for temporal causal discovery. While existing work assumed independent noise, the new result here allows for history-dependent noise. The proposed structure identification method combines continuous optimization, variational inference, and deep neural networks. Empirical results on synthetic and real data show the applicability of the approach. The reviewers had concerns on the clarity and presentation on some of the results, most of which were addressed in the author response.
justification_for_why_not_higher_score: Presentation and clarity of some of the results need improvement
justification_for_why_not_lower_score: Interesting problem, solid method
Decision: Accept: notable-top-25%