Venue: CLeaR 2022 Conference

Reviews:

final_score: rating: 6: Marginally above acceptance threshold
review_content: Summary: Estimating causal structure area challenge in causality, especially in presence of unobserved variables. The authors first define a particular latent causal model, latent factor causal models, allowing the edges between observed variables and latent variables. Then, the authors propose a three-step method to estimate the model by making use of Tetrad constraints.  Although the work relies on strong assumptions, it appears to be both novel and significant.
Main review: The paper tackles a non-trivial task and proposes a novel method to estimate the causal structure under their problem setting. 
The paper builds on prior work in the field of Tetrad-based latent variables models. The authors put some effort into dropping the traditional measurement assumption and estimating the causal structure, including causal direction.
The authors have an in-depth understanding of the related works and provide a detailed review.


However, there are some concerns and suggestions,

1. The authors say that the casual order between clusters can be identified. Are there any theories to support this result? As far as I know, in a linear Gaussian setting, there is no possibility to detect the causal direction between variables, except the V-structure and Meek rules. 


2. The example of In Section 4: The Phase I of the algorithm firstly selects the cluster \{ X_1, X_2, X_3 \}. What is the reason? Why not is the \{ X_4, X_5, X_6 \}? It seems that those two clusters have the same Tetrad constraints.

Besides, the authors should firstly give the ground-truth graph. 
It would be helpful to describe the details of the example in the main graph.

3. In Section 5.2: How do you remove the direct effect of Raf on Mek? Why don't you do the same process for the edge between PLCy and PIP2? 


minor typos:
Figure 3: there are two variables X_7 subgraph (b) and (c);

If the authors sufficiently address the mentioned concerns I am happy to change my assessment.
review_title: null

final_score: rating: 6: Marginally above acceptance threshold
review_content: Summary: This paper tackles the problem of causal discovery in the presence of latent variables. Motivated by gene regulatory networks, the authors design a three-stage algorithm that is consistent under some conditions. Theoretical analyses are provided for the identiﬁability of results. Empirical evaluations are provided to verify the effectiveness of the proposed method in this paper. 
Main review: Pros:
(1)	The addressed problem is realistic and significant. 
(2)	Experiments results are convincing. 
Cons/Questions: 
(1)	The motivation is still not very clear. Specifically, the authors state that they would address the problem of causal discovery in the presence of unobserved confounders. They carefully discuss the two types of methods for handling this problem. However, why is the proposed method better? Could it address some issues of existing methods? In the current version, the answers are not clear. Therefore, it is a bit hard to understand the motivation and contribution of this paper well. Such explanations are important and should be added. 
(2)	This paper argues that one of the weaknesses of the existing methods is the rationality of assumptions. Nevertheless, it seems that the method in this paper needs more assumptions. How to check them? For Definition 1 and Assumption 1, 2, 3, there are not enough analyses, e.g., the application scenario. 
(3)	Could the authors add more details for Definition 1? For example, the discussions on Definition 1(b), the relationship between edges and the rank of sub-matrix. 
(4)	Is the complexity of the method in this paper is relatively high?
(5)	The descriptions of experiments can be improved. 
-	The descriptions of experimental settings are less logical, especially in Section 5.1. 
-	Discussions on experimental results are insufficient. 

In summary, this paper is appreciated. However, there are major issues/concerns listed above.
review_title: null

final_score: rating: 6: Marginally above acceptance threshold
review_content: Summary: The authors proposed a latent factor causal model with some restricted assumptions, which was motivated by gene regulatory networks. And they proposed a consistent three-stage algorithm to identify such a model. 
Main review: The authors proposed a latent factor causal model with some restricted assumptions, which was motivated by gene regulatory networks. And they proposed a consistent three-stage algorithm to identify such a model. Overall, I think the paper is written with some minor mistakes, but the motivation from the biology field is interesting. I have some concerns listed in the following.

1. The identifiability seems not to be clear. What actual identifiability results did they achieve? And to what extent they identify? Did the overall structure including the edges from the observed to the latent could be identified, or only the cluster? It is better to make them clarified. 

2. As for the [Double-parent assumption] in Definition 1, what would happen if there is only one observed variable X_i in C_k that points to L_{k’}? May be better to explain it and add this case in the synthetic experiments.
review_title: null

Meta-review: The authors propose a method for recovering a DAG from observational data with latent variables. For this to be possible, the authors must impose very strong assumptions on the structure of the latent and the observed variables. For instance, the authors assume no direct effects between the observed variables and no direct effects between the latents. They also make strong parametric assumptions (linear Gaussian SEM). The plausibility of these assumptions in general settings is questionable. However, the authors claim that their work is motivated by gene regulatory networks. The paper is well-written, the authors provide thorough references, and both theoretical and applied results are provided.

In my opinion, the work presented in this paper is important even though it focuses on a very narrow set of cases. Research into the causal discovery under some assumptions on the structure of latents is necessary to incorporate various kinds of domain-specific expert knowledge. As such, I am inclined to suggest this work for publication and see it as a starting point for future research on similar topics.
Decision: Accept (Poster)