Venue: CLeaR 2022 Conference

Reviews:

final_score: rating: 6: Marginally above acceptance threshold
review_content: Summary: This work is the first to work on relational causal models. It proposes \sigma-separation for such causal models and show it is sound and complete under relatively strong assumptions.
Main review: ## major comments
1. I wonder how meaningful it is to study causal models with cycles. Can we always decompose the variables s.t. the cycles can be avoided? For example, we can decompose performance into P1 and P2, then we let P1 be the cause of quality and P2 be the effect of quality.
2. It seems assumption 3 is likely to be violated in many cases. For example, in a standard probabilistic SCM, every observed variable would have an exogenous noise variable pointing to it.

## details
1. I think in definition 1 it should be d-separation instead of \sigma-separation.
2. There are many terminologies and notations introduced, it is better to have a table to summarize them.
3. It is better to intuitively introduce the difference between \sigma separation and d-separation with an example after introducing their definitions.
review_title: null

final_score: rating: 6: Marginally above acceptance threshold
review_content: Summary:  
Main review: The focus of the work is on relational causal models, which generalize over previous causal models by capturing interactions between non-iid instances. A causal representation named abstract ground graph (AGG) was previously introduced for reasoning in relational models. But this representation does not allow for cycles. The contribution of this work is to generalize that line of work by extending the framework to allow for cycles. The authors introduce a presentation called sigma-AGG. Also introduce relational sigma-separation for reasoning about relational queries and show that it is sound and complete.

A clear motivation for using relational models is not presented and the advantage of using relational models over, say, chain graphs is not clarified by the authors. This paper is of interest only to readers sufficiently interested in the original papers on relational models.

The authors show that under Assumption 3, relational sigma-separation is complete. The authors have not clarified what is the interpretation of this assumption and what real-life models are excluded due to this assumption.

Definition 3 is not clear. What does it mean that dependencies construct cycles. At this point of the paper, nothing is said yet about the connection between the distribution and a cyclic graph. 

In general, the notion of cycle in relational models is not clear. In SCMs, we start with structural equations, and we obtain the edges based on those equations. Then those equation can result in cycles, which could be interpreted as steady state of the equations. What is the meaning of cycles in a relational model?
review_title: null

final_score: rating: 4: Ok but not good enough - rejection
review_content: Summary: This work generalizes the relational causal models to account for cycles by introducing "relational sigma-separation" based on the work of Forré and Mooij (2017). 
Main review: The most important problem with this manuscript is its lack of clarity. The concepts on which it builds, i.e. relational causal models and cyclic causal models, are non-standard and thus should be defined clearly to help the non-expert reader (like myself) undertand the contributions. I often had to refer to either Forré and Mooij (2017) and Maier et al. (2013b) to understand some notions specifically related to cyclic causal models and relational causal models.. This is not necessarily a bad thing given some notions are fairly complex and cannot be fully explained in the background section of a conference paper, but, once I understood the notion, it became clear that it could have been explained more clearly in the manuscript without eating up too much space. This lack of clarity prevents me from recommending acceptance at the moment.

### Originality:
To the best of my knowledge, cyclic relational causal models are novel and were not investigated before. That being said, most theoretical results in this paper seem to be rather direct applications of the results of Forré and Mooij (2017) and Maier et al. (2013b), which leads me to think this work has medium originality.

### Significance: 
The motivation for relational causal models was almost completely missing from the manuscript. In addition, the cycle between "employee.performance" and "product.quality" in the motivating example is never explained. As a result, the overall contribution of this work lacked motivation which led me to believe its significance is somewhere between low and medium. 

### Clarity:
- Related work is hard to follow for someone unfamiliar with relational causal models and cyclic models. Consider integrating it with the Preliminaries section.
- Definition 1: should be d-separation instead of sigma-separation.
- Section 3.4: This section was very hard to understand. Why are they more than one relational skeleton? The notion of "relational path" and "perspective" feels largely unmotivated. What is the difference between [Alice].salary and [Laptop, develops, Alice].salary? 
- In Figure 2, it would be useful to have a relational skeleton represented between the relational causal model and the ground graph.
- The explanation of an "abstract ground graph" (AGG) in Section 3.5 was very fast given its central importance. After reading about it in Maier et al (2013b), I noticed that the definition in the present manuscript does not mention that the AGG is actually dependent on the perspective and the "hop threshold" h. This seems like an important point completely missed. This omission makes the relational counterpart for graphical d-separation in section 3.6 very confusing. Also, the notion of "intersection variables", which is important for later results, is very poorly explained. What does the reader should understand from "Intersection variables are constructed from pairs of relational variables with non-empty intersections."? The intersection of relational variables was never defined.   
- Definition 5 what is s(B)? Couldn't find the definition.
- Definition 6: the hop threshold "h" appears for the first time next to a AGG, without any prior explanation. Also, points 1.b and 2.b are not clearly explained. The former refers "intersection variables" which were ambiguously defined and the latter uses "inherit" in a very vague sense.
- Shouldn't Definition 7 be a theorem or a proposition?
	

### Technical quality:
- I am not familiar with cyclic causal models, but the paragraph starting with "Spirtes (1995); Neal (2000)" just after definition 1 was confusing. It says that d-separation are not sufficient to entail all the corresponding conditional independence relations in a direct cyclic graph. However, this statement is meaningless without formalizing a connection between the causal graph and the distribution via a Markov property or a structural causal model. For instance, in an acyclic causal model, we can assume that the distribution is entailed by an SCM with some graph G. Then, it is meaningful to talk about the relation between the graph G and the conditional independences in the distribution. 
- On a related note, it is mentioned nowhere how one should translate the cyclic graph into conditional independence statements. I suspect this is what Definition 2 is for: \sigma-separation implies corresponding conditional independence? It should be explicitly stated.
- The lack of clarity made reading the main theoretical contributions of this work very difficult. As a consequence, I could not assess their quality.

# Response to rebuttal 
I thank the authors for providing clarifications. I maintain my initial assessment: the lack clarity and motivation are the two main problems with this manuscript that prevent me from recommending acceptance at the moment. I encourage the authors to improve on these aspects in a future iteration of their work.
review_title: null

Meta-review: The paper develops an abstract representation to reason about relationships in relations models which may contain cycles. The paper proposes \sigma-separation for such relational causal models. The implication of the proposed work is that there can be directed cycles of arbitrary lengths which is an interesting contribution.

There are certain suggestions/improvements suggested by the reviewers, which could improve the readability of the paper:

(a) an example showing the difference between \sigma-separation and d-separation. (b) more discussion surrounding how the proposed framework is useful as compared to the scenario when the underlying dynamic process can be described through an acyclic causal graph over time (as a cycle can be unfolded in time to yield a directed acyclic graph).

I encourage the authors to improve the readability of the paper by taking into consideration feedback by the reviewers.

I believe the proposed abstract representation to reason about cycles is an important contribution, and would be appreciated by the community.
Decision: Accept (Poster)