Venue: NeurIPS 2022 Conference

Reviews:

final_score: rating: 5: Borderline accept: Technically solid paper where reasons to accept outweigh reasons to reject, e.g., limited evaluation. Please use sparingly.
review_content: summary: The paper proposed a new DAG constraints for low rank adjacency matrices. Compared to original DAG constraints, the new constraint can scale to larger graphs. On binary graph, the proposed DAG constraints is a necessary and sufficient condition for an adjacency matrix to form a DAG. However, for a weighted adjacency matrix, it seems that without further work, the proposed DAG constraint is a sufficient but not necessary condition. In that case the proposed method actually is optimising over a space that is smaller than the true DAG space.
strengths_and_weaknesses: The idea of the paper is very similar to [1], and [1] is rejected by ICLR2020 and now it is only a preprint. Unfortunately, the paper share the same fatal problem as [1]. Let us consider an adjacency matrix W = UV, if we enforce that 
When apply such low rank DAG constraints, it is easy to derive a necessary and sufficient condition on binary adjacency matrices. If W is a weighted matrix, then we have to first make the entries of W to be positive to apply the NOTEARS type DAG constraints. In this procedure, in order to use the low rank property, one has to apply absolute value, or square over entries of U and V. In that case, the DAG constraint becomes sufficient only.

The main result (Proposition 2) of the paper is actually trivial. The proof in the supplementary is over complicated. In fact the proof of this trivial result is very straightforward. For a matrix W \in R_{>=0}^{n\times n} = UV, where all entries of U and V are also no-negative, W is nilpotent if and only W is a DAG. Furthermore, VU is nilpotent if and only if UV is nilpotent, and thus VU is DAG is equivalent to UV is DAG.

There is also a minor problem. The rank of DAG graphs can be very large. For example, if we consider a chain structured DAG with n nodes, the rank of its adjacency matrix is n - 1. Thus the proposed method only suits sparse graph structures. 

Finally, in the identifiability section, the authors provide a theorem about the rank of the graph? How the the theorem related to the identifiability? Will this enforce the faithfulness of the discovered graph?
[1] Fang, Zhuangyan, et al. "Low rank directed acyclic graphs and causal structure learning." arXiv preprint arXiv:2006.05691 (2020).
questions: See my comments above.
limitations: 1. The main result is trivial and it is only an sufficient condition of DAG.
2. There may be no real identifiability result.
review_title: null

final_score: rating: 7: Accept: Technically solid paper, with high impact on at least one sub-area, or moderate-to-high impact on more than one areas, with good-to-excellent evaluation, resources, reproducibility, and no unaddressed ethical considerations.
review_content: summary: This paper proposes an approach to causal discovery in high dimensional settings where interventional data is available. The authors use a low-rank assumption on a factor graph, and incorporate the model into a differentiable causal discovery algorithm by utilizing a likelihood model which assumes perfect interventions. Empirical results show strong performance with respect to prior art.
strengths_and_weaknesses: Strengths:

* The introduction of a method that allows for a low rank factor assumption is very nice, and provides a valuable tool in causal discovery where sparsity can be a difficult assumption to enforce.
* The approach is a nice and relatively simple solution to a difficult problem.
* The parameterization of the model with the Gumbel-softmax prior is quite nice.

Weaknesses:

* Unclear how the number of factors should be chosen. 
* Experimental evidence which shows the robustness to misspecification (both in terms of rank and the Gaussian assumption) would be helpful.
* (Minor) It would be good if the authors more clearly delineated that this paper deals solely with interventional data. 
questions: * Is there a parameterization that would allow for the rank to be chosen as well? Perhaps I am missing something along these lines.
* The work assumes perfect interventions in the likelihood. Would this line of work extend to imperfect interventions? Purely observational settings? It would be nice if the authors were able to clearly delineate within the text where the interventions are strictly required.
* Is it possible to have a set of experiments, as detailed above, that show robustness to misspecification?
limitations: The authors do a nice job of describing their work within the parameters of necessary assumptions and constraints. I don't foresee clear societal impact issues ehre.
review_title: null

final_score: rating: 6: Weak Accept: Technically solid, moderate-to-high impact paper, with no major concerns with respect to evaluation, resources, reproducibility, ethical considerations.
review_content: summary: This paper aims to solve the large-scale causal discovery problem with hundreds of nodes. To this end, the authors first introduce factor directed acyclic graphs (f-DAGs) which have many promising properties by incorporating the structural assumption to restrict the search space and reduce the optimization difficulty. Then, they propose Differentiable Causal Discovery of Factor Graphs (DCD-FG) to complete large-scale causal discovery. Theoretical analyses and experimental results demonstrate the superiority of f-DAGs and DCD-FG.
strengths_and_weaknesses: Strength:
1. This paper effectively reduce the search space in the large-scale causal discovery problem by introducing factor directed acyclic graphs. Based on which they propose Differentiable Causal Discovery of Factor Graphs to realize scalable causal discovery.

2. The experiments are well designed. This paper provides runtime experiments, simulation studies, and a case study on single-cell RNA sequencing data with hundreds of genetic interventions to demonstrate the efficacy of the proposed method.

Weakness:
1. It seems quite confusing in line 41-44. In the first sentence, it says “sparsity [17] as well as low-rank assumptions [18] are often exploited in algorithms”. However, in the next sentence, it points out “the use of low-rank constraints remains largely under-explored for this purpose”.

2. The theoretic property of this work is not well presented. The proposition 1 is only a very special case of lpw rank models. It would be better to justify the method in a wider scenarios.

questions: 1. How to justify that the low rank assuption is commonly met in real scenarios?

2. Although intuitively making sense, is there a theoretical result for the claim that "more statistically robust in the high-dimensional regime where the underlying skeleton is hard to assess"?

3. It seems most experimental results suround the SHD, and F1 score. Since your claim is fast searching, can you also show some computational efficiency results? 
limitations: There are no  limitations and potential negative societal impact of their work.
review_title: null

Meta-review: metareview: In this paper, the authors propose a new DAG constraint for low-rank adjacency matrices., which can scale to larger graphs. All the reviewers consider this paper is sound and the experiments are well designed. However, one question about the case of different graph spaces from other reviewer should be addressed in the final version.
confidence: Certain
Decision: Accept