Interpretability and transparency are essential for incorporating causal effect models from observational data into policy decision-making. They can provide trust for the model in the absence of ground truth labels to evaluate the accuracy of such models. To date, attempts at transparent causal effect estimation consist of applying post hoc explanation methods to black-box models, which are not interpretable. Here, we present BICauseTree: an interpretable balancing method that identifies clusters where natural experiments occur locally. Our approach builds on decision trees with a customized objective function to improve balancing and reduce treatment allocation bias. Consequently, it can additionally detect subgroups presenting positivity violations, exclude them, and provide a covariate-based definition of the target population we can infer from and generalize to. We evaluate the method's performance using synthetic and realistic datasets, explore its bias-interpretability tradeoff, and show that it is comparable with existing approaches.
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Summary
The paper addresses the overlap violation problem in observational datasets for causal inference by presenting an interpretable balancing method for overlap violation identification and causal effect estimation for binary treatments. The method BICauseTree adapts decision tree classifiers to the stated problem by recursively splitting the data population into non-overlap-violating subgroups based on covariate dissimilarity and treatment heterogeneity. The major advantage of the presented method in comparison to existing balancing methods is the interpretability of the prediction process.
Strengths
• The authors evaluate their method on both synthetic and real-world benchmarking datasets.
Weaknesses
- The proposed method is highly similar to the work in reference 12. Furthermore, related work is not discussed appropriately (section 2). It is thus unclear how this work significantly differs from previous contributions in the literature. The originality of the submission has to be considered very limited. - The manuscript presents a complete piece of work. Claims about the performance of the proposed method are supported by experimental results. Nevertheless, the an experimental study with sophisticated baseline methods is missing. A performance comparison with a Causal Forest model would be desirable. - Claims aiming at motivating the method are neither supported quantitatively nor experimentally (e.g., an analysis with different levels of overlap violation; unbiased estimation). - The submission lacks clarity due to multiple grammar errors and many nested arguments. The mathematical notation (section 3.1) lacks formal correctness. - The citation style does not agree with the required format for NeurIPS submissions. - The statement of a high ASMD indicating a confounder (line 164) needs to be justified. - The paper would profit from a revision of the language and the consistency of the presented arguments (e.g., lines 84, 181/182). Furthermore, the figures and sections need to be referenced correctly, as also recognized by the authors in the appendix. - The authors claim interpretability of the method but do not provide evidence for the statement. Here, a user study would be desirable etc. - The method is limited to ATE.
Questions
- What is the major difference between the method BICauseTree to the existing method PositiviTree (reference 12)? The novelty of the method cannot be deducted from the manuscript. - How do the benefits of the presented method outweigh the negative impact of the information loss due to the "prediction abstention mechanism"? A quantitative assessment would be of interest.
Rating
3: Reject: For instance, a paper with technical flaws, weak evaluation, inadequate reproducibility and incompletely addressed 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
1 poor
Presentation
1 poor
Contribution
1 poor
Limitations
- The authors have stated the limitations of their work. The section could be improved by highlighting the general weaknesses of single trees in prediction settings which naturally devolve to the proposed method.
Summary
This paper proposes a new method called BICauseTree for interpretable causal effect estimation. BICauseTree is a hierarchical bias-driven stratification method that identifies clusters where natural experiments occur locally. The method is designed to reduce treatment allocation bias and improve interpretability. The authors evaluate the performance of BICauseTree on several datasets and compare it to existing approaches. They find that BICauseTree performs well in terms of bias-interpretability tradeoff and outperforms existing methods in some cases. Overall, the paper presents a novel and promising approach to causal effect estimation that could have important applications in various fields.
Strengths
1. Novelty: The paper proposes a novel method called BICauseTree for estimating causal effects from observational data. The method is based on a hierarchical bias-driven stratification approach that identifies clusters where natural experiments occur locally. The method builds on decision trees to reduce treatment allocation bias and provides a covariate-based definition of the target population. The method is interpretable and outperforms other state-of-the-art methods in reducing treatment allocation bias while maintaining interpretability. 2. Significance: Causal effect estimation from observational data is an important analytical approach for data-driven policy-making. However, due to the inherent lack of ground truth in causal inference, accepting such recommendations requires transparency and explainability. The proposed method addresses this issue by providing an interpretable and unbiased method for causal effect estimation. The method has the potential to be applied in various domains, including healthcare, social sciences, and economics. 3. Experimental Evaluation: The paper provides a thorough experimental evaluation of the proposed method using synthetic and realistic datasets. The authors compare the performance of their method with other state-of-the-art methods and show that their method has lower bias and comparable variance. They also conduct sensitivity analyses to evaluate the robustness of their method to violations of the assumptions. The experimental evaluation provides strong evidence to support the claims made in the paper.
Weaknesses
1. Limited Scope: The paper focuses on a specific method for causal effect estimation from observational data, and the scope of the paper is relatively narrow (especially related to the tree-based models). While the proposed method is novel and has some advantages over other methods, it may not be of interest to a broad audience: (1) The method relies on the quality of the data and the assumptions made in the model. If the data is noisy or contains missing values, the method may produce biased estimates.; (2)The method may not be suitable for high-dimensional data, as the number of covariates may increase the complexity of the decision tree and lead to overfitting; (3) The method may not be suitable for datasets with small sample sizes, as the stratification may lead to small sample sizes in some subgroups, which may affect the accuracy of the estimates;(4)The method may not be suitable for datasets with complex interactions between the covariates, as the decision tree may not capture these interactions effectively. 2. Experimental Evaluation: While the paper provides an experimental evaluation of the proposed method, the evaluation is limited in scope and does not provide a comprehensive comparison with other state-of-the-art methods. The experimental evaluation would benefit from a more comprehensive comparison with other methods (such as TARNet from the machine learning domain) and a more detailed analysis of the results.
Questions
In Figure 1, the IPW looks very close to the BiCausalTree. How can we apply post hoc explanations in such cases in general?
Rating
5: Borderline accept: Technically solid paper where reasons to accept outweigh reasons to reject, e.g., limited evaluation. Please use sparingly.
Confidence
3: You are fairly confident in your assessment. It is possible that you did not understand some 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
3 good
Limitations
See weakness.
Summary
This paper focuses on achieving interpretable causal effect estimation, where the goal is to ensure that each decision within the algorithm is explicit and traceable. The authors propose a decision tree-based balancing method to address this problem, which identifies clusters where local natural experiments occur. The effectiveness of the proposed algorithm is empirically evaluated using synthetic and semi-synthetic data. The paper also did several ablation studies on the trade-off between interpretability and bias and the consistency of the decision tree.
Strengths
Overall, this paper is well-executed and demonstrates several notable strengths. - This paper is very clear. It effectively presents complex ideas in an easily understandable manner. - The problem addressed in the paper is well-motivated and interesting. - The authors display a strong grasp of the related work in the field, effectively positioning their contribution within the existing literature. - The empirical analysis conducted in the paper is thorough and yields valuable insights. - The method is intuitive and well explained.
Weaknesses
- Style file: One issue with this paper is that it doesn't follow the NeurIPS style guidelines, specifically regarding paragraph spacing. The paragraphs are not well-separated, which makes it harder to read and understand the content. This affects the overall flow and coherence of the paper. Additionally, the excessive content allowed due to the spacing issue may be seen as unfair to authors who followed the style guide correctly. This may be a potential ground for rejection. - Method: The rationale behind considering features with the highest ASMD as potential confounders is not well-explained. This is an important assumption in the paper, but it lacks a clear justification or empirical investigation. Providing additional explanations or conducting empirical studies would strengthen this aspect of the paper. - The experiment section of the paper is not self-contained. Although the motivating problem revolves around identifying subpopulations with natural experiments, this aspect is not adequately illustrated in the experiment section. Instead, the focus is primarily on bias analysis, with the analysis related to interpreting the causal effect estimation process deferred to the appendix. This undermines the fulfillment of the paper's fundamental promise to the readers. To address this issue, it is highly recommended that the authors integrate the analysis into the main paper, ensuring that the key components align with the paper's core premise.
Questions
Why does a feature with high ASMD more likely to be a confounder?
Rating
6: Weak Accept: Technically solid, moderate-to-high impact paper, with no major concerns with respect to evaluation, resources, reproducibility, ethical considerations.
Confidence
3: You are fairly confident in your assessment. It is possible that you did not understand some 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
3 good
Limitations
n/a
Summary
The paper introduces a decision tree methodology to identify regions where selection bias no longer ensures covariate balance. These regions, which have some level of interpretability, can then be removed in subsequent analysis.
Strengths
The paper presents an interesting decision tree methodology. The paper contains a significant amount of simulation experiments to validate the procedure.
Weaknesses
Despite a focus on covariate balance, there is no guarantee of balance unlike competing methods (rerandomization, matching, etc). Furthermore, there is limited analysis to show the claims of balance are fulfilled, especially for high dimensions. The paper explores a bias-interpretability tradeoff, but provides no rigorous definition. The proposed model often is more biased than alternative models, most notably IPW, and it's not clear that the resulting decision trees, or their interpretations, are actually sensible. No discussion of estimator variance is given or how that might factor into a tradeoff, despite the high variance generally expected from decision tree estimators.
Questions
In Section 2, it is briefly claimed that BICauseTree is better suite for ATE estimation instead of CATE, with no further discussion. This feels like a potentially important point and requires further justification. Trimming has the potential to bias treatment effect measurement. Are there any guarantees that trimming in your model ensures unbiased estimates? Are the decision trees in Figures A13 and A17 interpretable? While the decision tree can be followed, the trimmed regions seem to have limited clinical interpretation. More discussion around this feels necessary. In particular, interpretable does not seem to imply correctness for this method. ASMD is often minimized to establish balance. While splitting on variables that exhibit high ASMD should generally lead to some level of balance, is there any guarantee that the resulting regions will be optimally balanced in any sense?
Rating
3: Reject: For instance, a paper with technical flaws, weak evaluation, inadequate reproducibility and incompletely addressed ethical considerations.
Confidence
3: You are fairly confident in your assessment. It is possible that you did not understand some parts of the submission or that you are unfamiliar with some pieces of related work. Math/other details were not carefully checked.
Soundness
1 poor
Presentation
2 fair
Contribution
2 fair
Limitations
The paper touches on some limitations, most notably the increases bias that is expected. The paper does not discuss the variance of the estimator in detail relative to other methods, which is another potential limitation. The method advocates for trimming nodes that violate positivity. These nodes could contain sensitive subpopulations and could lead to fairness concerns.
The authors addressed and clarified the main questions and weaknesses. Nevertheless, the novelty of the work is still highly limited and the justification for statements supporting the method needs to be improved. Overall, I therefore raise the rating score by one point, but still consider the work insufficient for a major contribution to NeurIPS. I think my comments above will be very helpful for revising their paper. Given that the authors are only brief in their rebuttal on the differences with [12], I suggest that they also have more technical deep-dive in the appendix. As I stated above, it would be nice to see some insights in line with the motivation (e.g., plotting a tree as a case study).
Thank you for the response
``the covariate with the highest ASMD is most likely to cause the most confounding bias, and therefore adjusting for it will likely minimize the residual confounding bias the most.`` This claim is not obviously true to me. Is there a proof, empirical studies, or existing work that demonstrates that?
We are not aware of existing work that demonstrates this, but it is well accepted in the field, and we believe this behavior can be easily simulated. The following code snippet shows that adjusting for the confounder with the larger imbalance (larger ASMD) results in lower estimation bias of the treatment effect, i.e., less confounding bias (since confounding is the only source of bias in this case). In contrast, adjusting for the confounder with the smaller ASMD results in far more biased treatment effect estimation, i.e., the residual confounding bias left is larger. ```python import numpy as np import pandas as pd import statsmodels.api as sm def generate_data(N=1000, seed=0): rng = np.random.default_rng(seed) a = rng.binomial(1, 0.5, size=N) X = rng.normal(0, 1, size=(N, 2)) X[a==1, 1] += 2 # x1 has larger discrepancy between treated and control units y = X[:, 0] + X[:, 1] + a X = pd.DataFrame(X, columns=["x_smallASMD", "x_bigASMD"]) a = pd.Series(a, name="a") y = pd.Series(y, name="y") return X, a, y def calculate_asmd(X, a): is_treated = a == 1 X1 = X.loc[is_treated] X0 = X.loc[~is_treated] smds = (X0.mean() - X1.mean()) / np.sqrt(X0.var() + X1.var()) asmds = smds.abs() return asmds X, a, y = generate_data() data = X.join(a).join(y) calculate_asmd(X, a) >>> x_smallASMD 0.031651 x_bigASMD 1.386414 # Adjusting for both covariates retrieves the true effect: print(sm.formula.ols("y ~ x_smallASMD + x_bigASMD + a", data=data).fit().params["a"]) # 1.00 # Adjusting for the more-biased covariate leads to a result somewhat closer to the true effect: print(sm.formula.ols("y ~ x_bigASMD + a", data=data).fit().params["a"]) # 0.92 # Adjusting for the less-biased covariate leads to high estimation bias print(sm.formula.ols("y ~ x_bigASMD + a", data=data).fit().params["a"]) # 2.98 ``` Additionally, this comment touches on an important point, further suggested by the above demonstration. Future work can combine the covariate-outcome associations with the ASMD in order to select the best candidate for splitting. For example, multiplying the ASMD of covariate _j_ with the absolute regression coefficient of (a standardized) covariate _j_, and selecting the covariate maximizing this combined value. we considered this approach, but decided against it in order to obtain an outcome-agnostic method.
thanks for the reply
The authors addressed all my concerns and I would like to keep my positive score.
Thank you for your detailed reply. Most of my concerns have been addressed to some degree, although I still have significant concerns: - I acknowledge that balance is a secondary concern to the primary goal of unbiassdness. That said, BICauseTree is explicitly referred to as an "interpretable balancing method". The lack of any type of guarantee, for balance or unbiassdness in general, along with unconvincing empirical results, remains a significant concern for me. - The lack of a rigorous definition of interpretability, or the bias-interpretability tradeoff, makes any claims of interpretability difficult to evaluate. Our difference of opinion in the interpretability of Figures A13 and A17 further reinforces this. - Furthermore, I still do not fully understand how the improved interpretability of excluded observations prior to ATE estimation will significantly aid a practitioner. Is it even an ATE estimator at that point? Is your focus on situations where a CATE estimator is impractical? I believe further discussion of the practical implications of BICauseTree is necessary. Ultimately, after reviewing your response, and the feedback of my fellow reviewers, I will not be changing my initial score at this time.
Thank you for your additional consideration and the points brought up. Please see our point-by-point response: * We understand the reviewer's concern about the lack of analytical guarantees and are only left with restating the fact that neither do other well-known modern methods [1 (a NeurIPS paper too), 2] that show their utility using simulations alone. If the reviewer can suggest specific experiments they would like to see to further convince them, then we will be happy to conduct them. * We operate within the page-limit constraints, and we acknowledge we might have been terse on some definitions we thought to be either well-established, intuitive, or can be deferred to external resources. For example, we describe interpretability based on Cynthia Rudin's landmark paper [3] and further refer to it. In her paper, she claims that _"Interpretability is a domain-specific notion so there cannot be an all-purpose definition"_ and that it is basically a useful constraint that _"obeys structural knowledge of the domain"_. We further believe that the fact we can discuss whether the _content_ of the explanation makes sense is a big step forward as this discussion is not even possible to begin with under any other black-box model. * The positivity assumption is one of the three assumptions required in order to make valid data-driven causal claims (in addition to causal consistency and exchangeability). However, in real-world data, not all units are always comparable to begin with, as they may have no counterparts in the other group to allow extrapolation of the outcome across groups. It is a very common in practice to discard these units [4, 5]. However this indeed changes the actual eligibility criteria and therefore to whom we believe the results will generalize to in the population. This is the reason why it is of interest to know on whom exactly the causal claims are made. The overlapping region is where a researcher believes their results will transport from the sample to the population (i.e., for whom the results are externally valid) [6]. When we discuss transportability, the "ATE" is indeed not well-defined, and need to be separated to the sample ATE (SATE) and the population ATE (PATE) [7, 8]. Lastly, the CATE is not a concern in this study. We again stress the ATE is a valid estimand on its own. For example, it has both logistical and philosophical justification in the field of public health policy. [1] Shi, Claudia, David Blei, and Victor Veitch. "Adapting neural networks for the estimation of treatment effects." Advances in neural information processing systems 32 (2019). [2] Hill, Jennifer L. "Bayesian nonparametric modeling for causal inference." Journal of Computational and Graphical Statistics 20.1 (2011): 217-240. [3] Rudin, Cynthia. "Stop explaining black box machine learning models for high stakes decisions and use interpretable models instead." Nature machine intelligence 1.5 (2019): 206-215. [4] Potter, Frank J. "The effect of weight trimming on nonlinear survey estimates." Proceedings of the American Statistical Association, Section on Survey Research Methods. Vol. 758763. Washington, DC: American Statistical Association, 1993. [5] Cole, Stephen R., and Miguel A. Hernán. "Constructing inverse probability weights for marginal structural models." American journal of epidemiology 168.6 (2008): 656-664. [6] Oberst, Michael, et al. "Characterization of overlap in observational studies." International Conference on Artificial Intelligence and Statistics. PMLR, 2020. [7] Degtiar, Irina, and Sherri Rose. "A review of generalizability and transportability." Annual Review of Statistics and Its Application 10 (2023): 501-524. [8] Imai, Kosuke, Gary King, and Elizabeth A. Stuart. "Misunderstandings between experimentalists and observationalists about causal inference." Journal of the Royal Statistical Society Series A: Statistics in Society 171.2 (2008): 481-502.
Decision
Reject