Go to TMLR homepageGraphGini: Fostering Individual and Group Fairness in Graph Neural Networks
Abstract: Graph Neural Networks (GNNs) have demonstrated impressive performance across various tasks, leading to their increased adoption in high-stakes decision-making systems. However, concerns have arisen about GNNs potentially generating unfair decisions for underprivileged groups or individuals when lacking fairness constraints. This work addresses this issue by introducing GraphGini, a novel approach that incorporates the Gini coefficient to enhance both individual and group fairness within the GNN framework. We rigorously establish that the Gini coefficient offers greater robustness and promotes equal opportunity among GNN outcomes, advantages not afforded by the prevailing Lipschitz constant methodology. Additionally, we employ the Nash social welfare program to ensure our solution yields a Pareto optimal distribution of group fairness. Extensive experimentation on real-world datasets demonstrates GraphGini's efficacy in significantly improving individual fairness compared to state-of-the-art methods while maintaining utility and group fairness.
Submission Length: Long submission (more than 12 pages of main content)
Changes Since Last Submission: ## Response to Action Editor
Dear Action Editor,
Thank you for your valuable comments and for the careful attention given to the details of our manuscript. We sincerely appreciate your constructive feedback. Below, we provide a point-wise summary describing how we have addressed your comments in the revised version of the manuscript.
### Response to commnets
1. > * **One issue is around the novelty of the term $Tr(Z^\top L Z)$, which I agree with the reviewer does appear to have been used in prior work such as InFoRM. Where I differ with the reviewer is that I believe it is a fine contribution to reuse it as part of a larger system with new theoretical motivation and connections. However, if this is the case the paper needs to be more explicit that the analysis and not the loss itself is the new contribution with appropriate citations to prior work. There is a bit of ambiguity about this in the discussion where the authors commented that this loss "may appear structurally similar" implying that it is actually different in some way............**
>Ans: We have added a discussion on page 7, immediately following the proof of Proposition 1, to address this point.
>*"The upper bound in Proposition 1 has appeared as a heuristic individual fairness regularizer in prior work. Here, we present a new interpretation based on the Gini coefficient."*
2. > * **A related issue is the relative merit of Proposition 1 and the current analysis relative to the reviewer's proposal of directly defining the vector-valued version using the 2-norm. While I am not sure I agree, I credit the reasonableness of the authors' position that the 1-norm version better captures the desired notion of fairness..........**
> Ans: We have included an additional footnote on page 5 for clarification.
> "*1 Here, the definition is expressed using the $\ell_1$-norm; alternative choices such as the $\ell_2$-norm are possible but correspond to different interpretations of fairness.*"
3. > * **Relatedly, I'm not entirely convinced that Proposition 1 is correct as stated. The proof includes the claim that "the denominator in Eq. 3 only scales the numerator and does not affect the inequality." But can't scaling the numerator by a sufficiently small constant (less than 1) cause the inequality to be violated? If there is some reason this doesn't happen the explanation should be made clearer.......**
Ans: We have addressed this concern by revising the explanation and making it more explicit after Equation (8).
"*as the denominator in Eq. 3 is strictly positive and scales both sides of the inequality, thereby does not affect the inequality.*"
4. > * **Proposition 2 currently lacks any motivation or discussion, which should be added to justify its inclusion. I am not sure what this would look like for the third claim of Proposition 2 which seems true but irrelevant to me. Since this is one of three component losses it will never be exactly minimized, so I don't see why a claim about what would happen if we did is relevant. Indeed, as the proof shows the minimizers are trivial........**.
Ans: We have added a discussion before Proposition 2 to improve the flow and motivation.
"*Next, we discuss the effectiveness of minimizing this differentiable upper bound as a surrogate for the true Gini coefficient. The following proposition outlines how optimisation over the relaxed objective remains aligned with reductions.....*"
5. >* **One final separate issue is that the claims in the conclusion are a bit strong and should be toned down. In particular there is no real evidence that "This particular way of using Gini is likely to have a major impact on future research". A version claiming it "may be of interest" would be more measured. Given that the use of GradNorm was removed from the list of major contributions, the sentence "Unlike existing state-of-the-art methods, the GraphGini automatically balances all three optimization objectives—utility, individual fairness, and group fairness—eliminating the need for manual tuning of weight parameters." should either be removed as well or rephrased ..........**
Ans : We have toned down the discussion related to GradNorm in the conclusion to better reflect its role in the paper.
"*We also demonstrate that the gradient-normalization-based technique (GradNorm) provides an effective way to balance utility, individual fairness, and group fairness objectives in graph learning, mitigating the need for extensive manual tuning of objective weights.*"
### Additional Comments
>* **1.2 still refers to four key innovations where there are now three**
>* **3.5 now starts with "Convergencey" which I assume is meant to be Convergence.**
Ans: We have carefully fixed both points mentioned above in the final draft.
**Thank you once again for your insightful comments, which have helped improve the clarity and quality of the manuscript.
Sincerely,
Authors**
Video: https://www.youtube.com/watch?v=uICma3XrZgs
Code: https://github.com/idea-iitd/GraphGini
Assigned Action Editor: ~Ian_A._Kash1
Submission Number: 5342
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