Front-door Adjustment Beyond Markov Equivalence with Limited Graph Knowledge

Summary

Causal effect estimation from data often requires assumptions about the causal relationships, either through explicit causal graph structures or implicit conditional independence statements. When confounding exists, the front-door adjustment becomes important for estimating the causal effect of treatment on the outcome using post-treatment variables. This paper studies testable conditional independence statements to compute causal effects using a front-door-like adjustment without knowing the graph under limited structural information. The effectiveness of the method is demonstrated through experiments on both random graphs and real-world causal fairness benchmarks.

Strengths

1. The proposed method enables estimating causal effects without requiring knowledge of the causal graph. Instead, it utilizes front-door-like adjustments based on post-treatment variables, making it applicable even in scenarios with unobserved confounding. 2. The proposed method relies on conditional independence statements that can be directly tested from observational data. This allows for identifying causal effects using observable information without the need for specifying the entire causal graph. 3. The proposed method requires only limited structural side information, which can be obtained from an expert. This requirement is less demanding than specifying the entire causal graph, making the approach more practical and feasible.

Weaknesses

1. The algorithm presented in the paper relies on stronger assumptions, but the paper does not mention them, raising doubts about the soundness and completeness of the proposed method. My main doubts are listed in the Questions. 2. Figure 5 appears to have a mislabeled Y-axis. It seems to be "Average ATE errors". Minors: Line 59, criteria -> criterion

Questions

1. Assumption 1 alone may not be sufficient. It might also be necessary to explicitly state that variable y is not a child node of variable t. 2. TTheorem 3.1 appears to be incomplete. For example, we have $t\rightarrow b\rightarrow y$ and $t\leftrightarrow y$, where $\leftrightarrow$ denotes a latent confounder. In this case, b is a cause of y, and the conditional independence between b and y may no longer hold. 3. Some cases present challenges in identifying P(Y|do(t=t)) due to the complexity introduced by latent confounders. It is unclear how to exclude these non-identification cases and handle them appropriately.

Rating

5: Borderline accept: Technically solid paper where reasons to accept outweigh reasons to reject, e.g., limited evaluation. Please use sparingly.

Confidence

4: You are confident in your assessment, but not absolutely certain. It is unlikely, but not impossible, that you did not understand some parts of the submission or that you are unfamiliar with some pieces of related work.

Soundness

2 fair

Presentation

3 good

Contribution

2 fair

Limitations

N/A

Summary

The authors proposed a method for estimating causal effects without requiring the knowledge of fully-specified causal graph, focusing on the case where unobserved confounding between treatment and outcome exists. This approach using a front-door-like adjustment formula has a novel contribution in that it can estimate causal effect using only simple structural side information which can be obtained from an expert and is less demanding than specifying the entire causal graph. The authors provide sufficiency proofs and demonstrate clear graphical criteria (a generalized front-door condition) for the proposed front-door-like adjustment formula.

Strengths

The authors present a generalized formula that accounts for the variability of the front-door criterion based on the structure of the graph. They provide sufficient conditions clearly for the formula and demonstrate its validity. Hence, in realistic scenarios where unobserved variables may exist between treatment and outcome, this methodology can be effectively utilized, proving its utility. In order to facilitate understanding for readers, the paper includes comprehensive prerequisite knowledge. it is anticipated that the formula proposed in this paper will have high utility.

Weaknesses

No specific weakness.

Questions

I once worked on the same problem a few years ago when I first read Entner’s paper on backdoor criterion but I had no luck. So I am super happy to read this paper! I am wondering whether you can compute the variance of ATE estimation for each selection of S so that we can make use of inverse variance weighting instead of simple average. Further, can you employ double machine learning like approach? (e.g., Jung et al. 2021, https://ojs.aaai.org/index.php/AAAI/article/view/17438) Suggestion: In consideration of the importance of Theorem 3.2 as a sufficient condition, it is recommended to include brief proof sketch not only in the appendix but also in the main body of the paper.

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.

Confidence

4: You are confident in your assessment, but not absolutely certain. It is unlikely, but not impossible, that you did not understand some parts of the submission or that you are unfamiliar with some pieces of related work.

Soundness

4 excellent

Presentation

3 good

Contribution

3 good

Limitations

The author clearly presents the limitations of the methodology proposed in Appendix A.2. As stated by the author, assumption 3 among the three assumptions is undoubtedly a strong assumption, which would require substantial domain knowledge to satisfy it in practical situations. Therefore, it is necessary to exercise caution and ensure sufficient attention when applying the methodology suggested by the author in experimental settings.

Summary

The paper investigates the problem of estimating the average treatment effect of variable "t" on variable "y" within the Pearlian framework. The paper proposes an algorithm that enables causal effect estimation using a front-door-like criterion while relying on only a limited knowledge about the underlying graph structure. The core of the algorithm lies in the search for a subset of obserables "z" that satisfies a series of independence criteria, thereby establishing a front-door-like formula using "z". The proofs employed in the paper leverage the do-calculus and the identifiability criterion of Tian and Pearl. In addition to its theoretical contributions, the paper also presents empirical demonstrations of the proposed approach across three distinct categories: (1) random Structural Causal Models; (2) synthetic data; and (3) real-world fairness benchmarks.

Strengths

The paper addresses an important problem in the field of causality research by examining the limitations of existing algorithms for causal effect estimation. It specifically aims at improving on the assumption of having access to the underlying causal graph, which is often not readily available. The main contribution of the paper is the introduction of a method for identifying a set of observables 'z' that enables the generation of a front-door-like formula, thereby improving causal effect estimation under limited graph availability. The paper presents a clear problem statement and provides well-presented proofs. By offering an alternative perspective on causal effect estimation, the paper provides valuable insights for tackling this challenging problem. Overall, the paper makes a meaningful contribution to the field and opens avenues for further research.

Weaknesses

One potential weakness of the paper is that once the requirement of designing a subset "z" satisfying the front-door-like criterion (Eqn (9)) is fixed, the proofs and the proposed independence criteria are relatively straightforward and achievable using the rules of do-calculus and the identifiability criterion. It is also not convincing to me how and why the exhaustive search runs fast for the random class of graphs generated in Section 4.1. The expected number of unobservables is of the order O(p), I am curious to know why the bidirected edges are chosen with probablity q/p? It would be convincing to see positive results for larger p with more unobservables. The in-completeness of the proposed algorithm and the mandatory requirement of Assumption 2 are the two major drawbacks of the paper (Please refer to Limitations for a detailed discussion.)

Questions

As pointed out by the authors, Assumption 2 is mandatory for the approach to work. This observation is not surprising but somewhat disheartening. It would be valuable to explore if there are any workarounds or alternative approaches to testing this assumption, possibly utilizing Confidence Interval (CI) tests. Given that the available knowledge is limited to only the children of "t," I am not sure if this is possible to test. Further exploration or discussion on potential alternatives or extensions to address this limitation would enhance the paper's robustness. Regarding the choice of the random class of graphs for the benchmark, it would be beneficial to have an explanation or justification provided in the paper. Understanding the rationale behind the class of graphs considered would provide more insights. I also suggest to provide a more detailed description of Algorithm 1 in the main paper, as that would enable readers to have a better understanding of the algorithm.

Rating

5: Borderline accept: Technically solid paper where reasons to accept outweigh reasons to reject, e.g., limited evaluation. Please use sparingly.

Confidence

4: You are confident in your assessment, but not absolutely certain. It is unlikely, but not impossible, that you did not understand some parts of the submission or that you are unfamiliar with some pieces of related work.

Soundness

4 excellent

Presentation

4 excellent

Contribution

3 good

Limitations

The primary limitation of the paper, in my opinion, is regarding the completeness of the algorithm. The fact that the proposed algorithm is not complete represents a significant drawback. A complete algorithm would have provided a more robust and comprehensive solution to the problem. As explained in the paper, Assumption 2 is crucial in order for the search to work which is another crucial downside of this approach. This reliance on a critical assumption may limit the generalizability of the approach to real-world scenarios where such assumptions may not hold. Indeed, I feel like finding a workaround or alternative approach to mitigate the reliance on Assumption 2 would greatly enhance the paper's technical as well as practical value. I believe issues regarding sample complexity are out of the scope of the paper and perhaps be considered for future work.

Summary

This paper proposes a method for estimating causal effects between the treatment variable and the outcome variable using front-door adjustment beyond the Markov equivalence class. This method is applicable when there are unobserved confounders between the treatment and outcome variables and does not require knowledge of the entire causal graph, but only limited graph knowledge. The authors introduce three assumptions and the causal identifiability theorem and the generalized front-door condition to achieve the estimation of the Average Treatment Effect (ATE). Through experiments, the paper demonstrates that the proposed framework provides identifiability in random fusion compared to PAG-based algorithms, exhibits lower error rates in ATE estimation compared to baseline, and shows practical applicability in causal fairness analysis.

Strengths

- The authors propose testable conditional independence statements for front-door-like adjustment without graph knowledge under limited structural side information. - The experimental results show that the proposed method is effective on random graphs and real causal fairness benchmarks.

Weaknesses

- It seems that the identification of the proposed method highly depends on Assumption 3. Assumption 3 requires knowledge of all direct descendant nodes $b$ of the treatment variables, which is too strong and difficult to achieve in practical scenarios. - Compared to PAG-based algorithms, the proposed method in this paper proves its ability to effectively provide identifiability. However, it requires expert knowledge to provide structural information, which may not necessarily demonstrate better applicability than PAG-based methods.

Questions

See above.

Rating

5: Borderline accept: Technically solid paper where reasons to accept outweigh reasons to reject, e.g., limited evaluation. Please use sparingly.

Confidence

2: You are willing to defend your assessment, but it is quite likely that you did not understand the central parts of the submission or that you are unfamiliar with some pieces of related work. Math/other details were not carefully checked.

Soundness

3 good

Presentation

3 good

Contribution

2 fair

Limitations

N/A

Response

Thanks for your response and clarification. I have read the authors' rebuttal and other reviewers' comments. I will maintain my rating.