Venue: NeurIPS 2022 Conference

Reviews:

final_score: rating: 3: Reject: For instance, a paper with technical flaws, weak evaluation, inadequate reproducibility and incompletely addressed ethical considerations.
review_content: summary: The paper studies the causal inference problem with interference under a linear model. It assumes known interference structure, and present conditions under which the bias due to ignoring interference is negligible. It also presents a linear regression method on a set of samples that satisfies the condition that no bias-inducing structures exist between any two distinct units.

strengths_and_weaknesses: I am not aware of many previous papers tackling this problem using the language/perspective that the authors use, so that seems something novel. On the other hand, my feeling is that the authors introduce too many terminologies so that the main idea is buried behind these notations.

The authors motivate the discussion with an example of COVID-19 but finish with a simulation (!) on student grades. Why not make it consistent? This is a simulation anyway.
questions: Is it possible to illustrate the main idea, and under what conditions you can identify/remove the bias, without resorting to these new terminologies you introduce? 

limitations: The linearity assumptions seem rather strong and do they ever hold in practice (for the whole network)?

Also the same for the other assumptions. More discussions on when one may be able to detect and remove the bias in a real context would be very helpful.
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 studies causal inference from non-iid data when there are interactions among units, in the case of linear causal relationships. In particular, it analyzes different types of interactions, detects and quantifies the corresponding interaction bias, and derives conditions under which it is safe to ignore interactions and estimate the causal effect with methods that are designed for iid data.
strengths_and_weaknesses: 
Strengths:
The studied problem is very interesting and meaningful because, in many real-world problems, the iid assumption is hard to hold. As far as I know, this work is original.

The authors show theoretical results on detecting and quantifying interaction bias, as well as a technique for removing the bias.

Weakness:
This paper does not seem easy to follow; there are too many definitions, and the writing also needs improvement. 

For the notation Xi, sometimes i is written as a subscript, but sometimes it is not.

The experimental studies do not seem enough.



questions: I would like to suggest the authors improve their writing. For experimental studies, it would be more convincing if the authors could consider different types of interactions that are considered in previous sections.
limitations: The authors did not discuss the limitations and potential negative societal impact of their work
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: The goal of the paper is to study non typical forms of interference that cause iid violation and bias, and how these affect Average Causal Treatment Effects estimates. Moreover the authors propose set of conditions which when they hold true, violation of iid assumption when using an algorithm meant for iid will result in negligible bias of the estimated ATE.

strengths_and_weaknesses: Strengths: 

The paper is well written  and with gradual introduction of the terminology needed for the reader. Also it addresses a very interesting statistical problem, relevant for many fields.

Weaknesses:

The interaction bias formula contains the variance of the root path node R_p. This means that the authors assume that R_p must be known in a real dataset.
I would like the authors to elaborate how realistic is this requirement, given that in many use cases the main problem is to identify the root cause of a target. 

I would like to see application on some real-dataset if possible. Also the comparison with Regression in the simulated graph is the absolute minimum. Could the authors include comparisons of their method with some state of the art ATE method?

Some comments about structure: 
- Captions of Figure 5, 6 and 7 cannot be read, as they are very close to each other. Please, add appropriate spacing.
- line 307, "some polots above' not 'below'.
- Minor typos: drop 'to' line 134, l.115 is -> are

questions: 
While the paper's ultimate goal seems very relevant for real datasets, i would like to ask the authors some questions about some points:
1. In Figure 5 I do not understand why figures 5c-5e do not contain a deflecting path as well. According to the open path definition (no collider), in all these graphs there is 
an open path from X_j to Y_i.

2. Does the proposed method assume that the user almost needs to know the full graph, and if so, don't we then already know if there is interference or not?

3. Could you please clarify what is meant by "no parameter i.e., S* is not an input" in line 207?
limitations: No limitations are discussed by the authors. I do not see any limitation with respect to societal impact for this work.
review_title: null

Meta-review: metareview: This manuscript offers some potentially important theoretical and practical contributions in the area of causal inference, particularly surrounding the assumption of iid data and how this assumption can be violated in the presence of interference. The manuscript describes a modeling framework for such interactions and derives some theoretical analysis regarding the detection such interactions and when they may be ignored (and the data nonetheless treated as iid). For a field experiencing considerable growth and momentum, these developments are timely and have a strong potential for impact.

Although there was some disagreement among the reviewers, the balance of opinion was in favor of acceptance, especially after the insightful author rebuttals and ensuing discussion between authors and reviewers. I recommend that the authors take the fruits of these discussions into account when preparing an updated version of this manuscript.
confidence: Less certain
Decision: Accept