Unfair Generalization in Graph Neural Networks (GNNs)

The proof of Theorem 2 demonstrates that GNNs tend to generalize better on test groups closer to the training set in structural distance. Through linear approximations and bounding loss functions, it shows that the difference in generalization performance between groups can be attributed to structural disparities, highlighting potential fairness issues in GNN applications.


This content originally appeared on HackerNoon and was authored by Computational Technology for All

:::info Authors:

(1) Junwei Su, Department of Computer Science, the University of Hong Kong and jwsu@cs.hku.hk;

(2) Chuan Wu, Department of Computer Science, the University of Hong Kong and cwu@cs.hku.hk.

:::

Abstract and 1 Introduction

2 Related Work

3 Framework

4 Main Results

5 A Case Study on Shortest-Path Distance

6 Conclusion and Discussion, and References

7 Proof of Theorem 1

8 Proof of Theorem 2

9 Procedure for Solving Eq. (6)

10 Additional Experiments Details and Results

11 Other Potential Applications

8 Proof of Theorem 2

Before diving into the detailed proof, we present an outline of the structure of the proof and prove a lemma which we use in the proof of the theorem. Outline of the proof for the thereom

\ 1. Suppose we are given Vi and Vj , two test groups which satisfy the premise of the theorem;

\ 2. Then, we can approximate and bound the loss of each vertex in these groups based on the nearest vertex in the training set by extending the result from Theorem 1;

\ 3. If we can show that there exists a constant independent of the property of each test group, then we obtain the results of Theorem 2.

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:::info This paper is available on arxiv under CC BY 4.0 DEED license.

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This content originally appeared on HackerNoon and was authored by Computational Technology for All


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