Counterfactual Fairness by Combining Factual and Counterfactual Predictions

Summary

This work studies the problem of counterfactual fairness in ML predictions. The authors first prove the form of the best possible fair predictor in a model-agnostic manner. Then, the excess risk of optimal predictor under the CF constraint is characterized. Based on the theoretical findings, the authors propose a post-preprocessing algorithm to achieve CF given arbitrary ML predictor. The authors perform comprehensive numerical studies to demonstrate the performance of the proposed algorithm compared to several baselines.

Strengths

1. The theoretical analyses throughout the paper are technically sound and comprehensive. 2. Presentation of the work is easy to follow and the writing quality is high.

Weaknesses

1. Although the authors acknowledges that the access to ground truth counterfactuals is out of the scope of this work, I personally think it is better to incorporate existing counterfactual estimation procedures into the Algorithm 1, which would enhance its practical applicability for the researchers and policy makers. 2. The authors can include more existing methods in the numerical experiments for comparison, such as the post-processing method by Wang et. al [1] and the pre-processing method by Chen et. al [2], to see the performance gap between these algorithms. [1] Wang, Yixin, Dhanya Sridhar, and David Blei. "Adjusting Machine Learning Decisions for Equal Opportunity and Counterfactual Fairness." Transactions on Machine Learning Research (2023). [2] Chen, Haoyu, et al. "On learning and testing of counterfactual fairness through data preprocessing." Journal of the American Statistical Association (2023): 1-11.

Questions

1. See Weakness 2. 2. Wang et. al [1] proposed a weighted average CF predictor and discussed the optimality of the proposed predictor, which shares similar spirit with this work. The authors can discuss the difference between this work and . Wang et. al [1]'s work in terms of accuracy and fairness guarantee. 3. Line 183; I am confused about the intuition about the objective function for counterfactual risk minimization (CRM). In my opinion, the counterfactual outcome may not be necessarily close to factual outcome $Y$. Can the authors explain more about the reason why adding the second term in the objective function? [1] Wang, Yixin, Dhanya Sridhar, and David Blei. "Adjusting Machine Learning Decisions for Equal Opportunity and Counterfactual Fairness." Transactions on Machine Learning Research (2023).

Rating

7

Confidence

4

Soundness

3

Presentation

3

Contribution

3

Limitations

The authors discuss the limitation of restrictive irreversible assumption in section 3 and access to ground truth counterfactuals and optimal predictors in section 6.

Summary

This paper focuses on counterfactual fairness in ML models (regardless of the model), which means that the prediction of the model should not change if the input individual had belonged to a different sub-population. The main contribution of this paper is to provide a theoretical trade-off between the performance of the model and counterfactual fairness.

Strengths

- The paper is very well written and well presented. It is easy to follow and understand the results. - The main strength of the paper is that it shows if we have access to the ground truth counterfactuals, using an unfair model (regardless of what model it is), we can achieve strong fairness and accuracy (Theorem 3.3). Later, they characterize the excess risk of the Bayes optimal predictor under the counterfactual fairness constraint (Theorem 3.4), which is again insightful.

Weaknesses

- Strong assumptions: access to the ground truth counterfactuals and access to the Bayes optimal predictor. However, they attempt to relax the first assumption slightly in Section 3.3. As I am not an expert in this field, I cannot verify how strong the assumptions (before or after relaxation) are and how practical they are.

Questions

- If A is not binary and is multi-class, what would the results of Theorems 3.3 and 3.4 look like? Specifically, in Theorem 3.3 where $x_a = G^*(x, a, 1-a)$, how can you rewrite this in a multi-class setting? - Again, in the multi-class case, what would the assumption of theorem 3.6 look like? Do you assume a bound on $G^*$ and $\hat{G}$ for every pair of A’s possible values?

Rating

6

Confidence

3

Soundness

3

Presentation

4

Contribution

3

Limitations

Yes.

Summary

This paper focuses on counterfactual fairness (CF), which is a promising framework for evaluating the fairness of machine learning models, and analyzes the trade-off between accuracy and CF. The authors give some theoretical results from the perspective of the Bayes optimal classifier under the perfect CF constraint. They also present theoretical analyses for cases where we can not access the ground truth of the causal structure and Bayes optimal classifier. The theoretical results in this paper were validated by experiments on synthetic and semi-synthetic datasets.

Strengths

- S1. This paper is easy to follow and well-organized. Each experiment seems to clearly correspond to what the authors want to validate. - S2. In Theorems 3.3 and 3.4, the authors analyze the predictive performance that can be achieved under the constraint of perfect CF from the perspectives of the Bayes optimal classifiers and their excess risk. I think the result that the excess risk of CF is completely characterized by the inherent dependency between Y and A as with the existing group fairness is interesting. - S3. The authors also give analyses for cases where we can not access the ground truth of the counterfactual generator (i.e., causal structure) and Bayes optimal classifier. Furthermore, they propose a simple learning framework, named CRM, that can be applied to both training from scratch and fine-tuning.

Weaknesses

- W1. I am concerned about the practicality of the proposed framework because the experiments in this paper seem insufficient. All the experiments in this paper seem to consider only one observed feature $X$. While these experiments may be sufficient to just validate the theoretical results, they seem too simple to demonstrate the reality and significance of the proposed framework. - W2. I am also concerned about the causal graph assumed in this paper. While there may be nothing wrong with assuming a causal graph like Figure 1 to show theoretical statements, I believe the behavior of the proposed framework in the case where this assumption is violated should also be verified by experiments. **---------- post-rebuttal ----------** I would like to thank the authors for their comments and clarifications. The author's rebuttal adequately addressed my concerns.

Questions

- Q1. Can the proposed framework be evaluated by the same experimental setting with [Zuo+ 23]? Their setting includes more complex datasets and causal models than those of this paper, and it seems to be applied to the experimental evaluation for the proposed framework of this paper. - Q2 (minor, optional). While the authors state "our analysis and our method can be naturally extended to multi-class $A$," I could not find how to do that in the paper including appendix. Is it trivial? And does it have no impact on the theoretical results? - Q3 (minor, optional). Can the proposed framework be adapted to the path-dependent CF constraint? [Zuo+ 23] Zhiqun Zuo, Mahdi Khalili: Xueru Zhang. Counterfactually Fair Representation. NeurIPS, 2023.

Rating

6

Confidence

2

Soundness

3

Presentation

3

Contribution

2

Limitations

Yes, the authors discussed the limitations and potential impacts of their work in Section 6 and Question 10 of Checklist, respectively.