Summary
This paper provided theoretical analyses for the accuracy-fairness trade-off and characterized the shape of the accuracy-fairness trade-off Pareto frontier (termed FairFrontier) for fair machine learning problems. The authors made an attempt to address a fundamental question “For a given data distribution, what would the accuracy-fairness trade-off curve look like?”. They leveraged synthetic data from known data distributions and constructed optimal classifiers to conduct examinations of the continuity of Pareto frontiers. Specifically, they characterized four different shapes of FairFrontier in terms of continuity and analyzed under what conditions these different frontiers will occur.
Strengths
The paper does introduce some new perspectives to the fair machine learning community. The main problems the authors attempted to address include:
- Two of the four Pareto front curves cannot occur, i.e., the sharp decline in fairness and the
sharp decline in both accuracy and fairness. (Lemma 1)
- When does a sharp decline in accuracy occur? (Lemma 2)
- When it is possible to maximize both accuracy and fairness simultaneously? (Theorem 1, Proposition 1)
- When do we expect to see a sharp decline in accuracy? (Theorem 2)
- When model unfairness and data unfairness are completely decoupled and additive? (Theorem 3).
Weaknesses
However, this paper should be rejected because (1) the theoretical analysis has limited novelty. (2) the theories developed in this paper are not solid and convincing. (3) the paper is imprecise and unpolished. (4) the insight to the real trade-off construction from the presented theories is limited.
Questions
**Main arguments**
1. The shape of Pareto fronts between accuracy and fairness is largely dependent on the model architectures and fairness metrics. Many research could be found in the literature that focuses on capturing the trade-off curve for different ML models. Ignoring imprecise presentation of Theorem 1-2, Theorem 1, and Proposition 1 convey a trivial argument that if optimizers for different sensitive groups are aligned, there is no conflict between fairness and accuracy. I cannot see enough novelty from there.
2. Theorem 2: if $T_\Theta^f$ is the optimal classifier for fairness, it corresponds to an extreme point on the global Pareto front with the lowest accuracy. I don’t see the possibility of the case where accuracy of $T^*_a$ is lower than that of the optimal classifier for fairness.
3. The statement of eliminating trade-offs is not rigorous. Also the authors didn’t give an actionable solution for aligning decision boundaries across different groups. Since the same accuracy classifier means the same decision boundary, can we just use the same classifier for different groups? In Proposition 1, the author basically formalized or rephrased when the accuracy-fairness conflict doesn’t exist. When the decision boundaries are identical across different groups, it means the sensitive attribute distributions are unbiased across positive and negative groups. If the distributions across different groups are biased, is it still possible to align decision boundaries with a separate classifier for each group? It is highly doubted.
4. Section 6.1 and 6.2: using the same setting, it is not clear to the readers how the two different shapes of the Pareto front in Figure 2 and Figure 4 were obtained.
5. Section 6.4: Example 4 in Figure 6, where is the claim “maximum accuracy becomes unattainable” based on? Again, the elimination of the accuracy-fairness trade-off doesn’t come from any changes in model architectures but comes from the natural optimization over accuracy. The example in Figure 7 seeing the same fairness and accuracy optimizer is due to the unbiased distribution of sensitive attributes across positive and negative groups.
**The paper has many imprecise parts, here are a few:**
1. Theorem 1 equation (7): Based on my understanding, it means the two groups are not discriminative at all.
2. Theorem 1 Condition 2: arithmetic operation over probability distribution function f(**) makes no sense.* f(*) is more like a mean function of nonsensitive feature vector, which limits the generality of the derived theory to any data distribution.
3. Theorem 1 P5 Condition 1: the equality between the 2nd and 3rd terms means basically the sensitive feature is completely aligned with target labels? In addition to (7), the theorem tried to convey that we can find a unique optimizer for both accuracy and fairness with completely random data samples from independent uniform distributions (for A and Y). I don’t see much useful insight from this theorem.
4. P6 second paragraph “a basic assumption in prior fair ML research that the loss function is convex”: the non-convexity of the Pareto front between accuracy and fairness doesn’t necessarily mean non-convexity of loss functions. The loss function is an estimation of accuracy and could be convex or non-convex depending on the ML models, while accuracy is a discrete measure.
5. P6 equation (12) what is the definition of $TPR^*$ and how it is computed are not clear.
6. Section 5 P7 the claim about how to tackle data unfairness doesn’t completely capture the root causes of data fairness. Other than data imbalance, there is inherent data bias from biased ground truth labels. There are a bunch of pre-processing based fair ML methods where the ground truth labels were re-labeled to reduce data bias.
**Things to improve the paper that did not impact the score:**
1. section 2 on p2 Notation: $\Theta$ in $T_{\Theta}$ is not introduced before use.
2. section 2 on p3 “FairFrontier is monotonically non-increasing” is misleading when describing a curve of two dimensions. From the point of view of accuracy, it is non-increasing, while in terms of fairness, it is non-decreasing. And the monotonicity is self-explained by the definition of Pareto fronts.
3. Figure 4 y axis label needs to be fixed.
4. P5 Section 4.2 second paragraph: “…the sign of the predictions is the same as that of the optimal classifier used for each group” → the optimal classifier for the whole dataset?
5. Figures 6-7 captions are misleading: both figures are demonstration for Example 4.
Rating
3: reject, not good enough
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.