Venue: CLeaR 2022 Conference

Reviews:

final_score: rating: 6: Marginally above acceptance threshold
review_content: Summary: The authors demonstrate that if additional assumptions are made on the vertices and the edges of a causal graph the resulting Markov equivalence class becomes much smaller. Their assumptions are: that vertices belong to predefined classes and causal relations can only be in one direction between any two classes.
Main review: The authors show that when a causal graph is assumed to be constituted of vertices belonging to specific types, and that edges are assumed to exist only in one direction between any two classes, the resulting Markov equivalence set for the data distribution in question becomes smaller. The authors' presentation is clear and easy to follow. This can be interesting for the researchers that focus on this topic. I also agree that this perspective can result in other useful results down the line with respect to integration of causality and machine learning research. 

On the other hand, I believe that the current paper's contribution to this cause borders on marginal. While the results can be useful for specific applications, in the paper's current state the extent of these applications seem to be limited. These limitations include the lack of an efficient algorithm for t-edge orientation, causal sufficiency assumption, the method inheriting (some) problems associated with cond. independence-based causal discovery methods, and lack of persuasive real applications. Perhaps an improved discussion of potential current applications and experiments on real datasets that indeed has type constraints would help the paper to better justify its arguments. Despite its shortcomings, I recommend the acceptance of the paper, given its potential downstream improvements by the related scientific community.

In addition to my comments above, I list some of the more specific comments and questions I have about the paper:
- How would the authors imagine their work to develop causal discovery in the presence of latent confounders?
- How does authors' theory and proposed algorithm work when we do not know the types of certain variables and/or when there is no constraint between certain pairs of variables in either direction?
- I think the concept t-edge is confusing. t-DAG is an augmented version of the original object (DAG). But t-edge is something completely different than the original object (a graph edge), i.e. while a t-edge is a set of edges, an edge is just a tuple. I would recommend using something similar to a t-edge-set. I imagine the authors think that this allows formulating the relationship between types as a higher-level DAG; but in its current state this terminology is more confusing than helpful.
review_title: null

final_score: rating: 7: Good paper, accept
review_content: Summary: This paper proposes a method for incorporating types into causal models, with corresponding causal structure learning algorithms for respecting typing assumptions. In short, if t1 and t2 are different types, then at most one type can cause the other. The utility of the method is shown in theory and in some test cases.
Main review: In my view this paper checks all of the boxes: it is well written and clear, the idea is a natural one, the results are largely convincing, and one is left wanting to know more. The central idea of the paper is very simple. It is not at all surprising that the kind of inductive bias the authors pinpoint would help in causal inference, simply by reducing the space of compatible causal graphs. But the authors go beyond this basic observation to clarify how exactly it will do so, and also give suggestive case studies in which the proposed algorithms really do appear to lead to gains. I also think the authors have a good argument for why this type of qualitative information is the kind of assumption that a domain expert might realistically be comfortable making.

Most of my questions about extensions and further comparisons are probably already on the authors’ radar. How does this work in the semi-Markovian setting (latent confounders)? What about other causal structure learning algorithms other than PC? And so on.

One point in the discussion that made me a bit nervous was the authors’ discussion of automated ways of discovering types. I could not tell from the discussion exactly what they had in mind here, but I believe it’s important that types in this context are not simply categories: rather, they have a substantive causal flavor. Without some further reason for thinking that categories in a given domain line up nicely with types that would support the relevant kinds of inference, I worry that trying to induce the types from correlational data could lead to systematic faulty inferences. Perhaps the authors could say a bit more about what they had in mind there?
review_title: null

final_score: rating: 8: Top 50% of accepted papers, clear accept
review_content: Summary: This paper develops a new class of graphical models called typed directed acyclic graphs. These tDAGs differ from DAGs in that each node is assigned a single type. Then, assuming that causal relationships between two types of variables arises in one direction, they develop Markov equivalence class theory for t-DAGs. This serves as the foundation for causal discovery, in which the authors modify the PC algorithm to handle types. Finally, the authors consider identification for random tDAGs.
Main review: Quality: The paper overall is of excellent quality. The technical exposition is up to the standard one would expect for a paper in causal discovery.
Clarity: This paper is very well written. The flow of the paper begins with interesting motivational ideas, and naturally opens into a formulation of the problem
Originality: To my knowledge, I have not seen DAGs approached in this particular manner. Similar techniques have existed (e.g. tiers in causal discovery) but none that restrict the equivalence class.
Significance: I believe this work will be significant to practitioners of causal discovery, since it develops tools that help incorporate additional information often present in applications.
Pros: The paper overall proposes a novel and interesting idea. The authors have done a good job developing and shaping that idea.
Cons: While I do think this work is a step in the right direction, I do wonder how often practitioners will find themselves in a situation where they can a) confidently partition variables into distinct types and b) have no idea how these types relate to each other. In my experience applying these methods, a) and b) tend to move together, since having a basic temporal ordering of variables is quite common in practice. 
The authors do address this partially by noting that types could be learned using ML classification methods, although this poses a further question of how exactly types might be identified from data (it is not immediately obvious to me that this identification task is trivial). 
Is it possible to incorporate some notion of uncertainty about types? The motivation here is that if I am unsure of how types relate to each other, I am probably also less sure of which variables belong to which type. Perhaps the authors may be able to sketch out a sensitivity analysis strategy that addresses this.
Minor notes:
I would consider using “collider” or “V-structure” in place of “immorality” as a more gender-neutral term.
review_title: null

Meta-review: This paper studies the problem of causal DAG discovery under an additional assumption: variables are typed and between two types of variables, causal relations, if any, are all of the same direction type-wise. The paper presents useful results on the size of an Markov equivalence class given the assumption, and shows empirically how this assumption, if warranted, can significantly improve the informativeness of causal discovery from observational data. These contributions are in my view sufficiently original and significant. Both the clarity and the technical quality are very good, as acknowledged by all reviewers.

A main worry concerns whether there are many real situations in which the typing assumption can be reasonably adopted. Although the authors made plausible arguments for the potential applications of their approach, real applications are yet to be made. The lack of experiments on real datasets is a notable drawback. Other, more minor concerns were raised in the reviewers' reports, to which the authors provided good responses.

Overall I agree with the reviewers that this paper is clearly acceptable. I also judge that it will be of interest to a relatively wide audience of this conference. I therefore recommend an oral presentation.
Decision: Accept (Oral)