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Towards Robust Fidelity for Evaluating Explainability of Graph Neural Networks

Xu Zheng, Farhad Shirani, Tianchun Wang, Wei Cheng, Zhuomin Chen, Haifeng Chen, Hua Wei, Dongsheng Luo

TL;DR

A formal, information-theoretic definition of explainability is introduced and it is shown that existing metrics often fail to align with this definition across various statistical scenarios, and a robust class of fidelity measures are introduced and it is shown analytically that they are resilient to distribution shift issues and are applicable in a wide range of scenarios.

Abstract

Graph Neural Networks (GNNs) are neural models that leverage the dependency structure in graphical data via message passing among the graph nodes. GNNs have emerged as pivotal architectures in analyzing graph-structured data, and their expansive application in sensitive domains requires a comprehensive understanding of their decision-making processes -- necessitating a framework for GNN explainability. An explanation function for GNNs takes a pre-trained GNN along with a graph as input, to produce a `sufficient statistic' subgraph with respect to the graph label. A main challenge in studying GNN explainability is to provide fidelity measures that evaluate the performance of these explanation functions. This paper studies this foundational challenge, spotlighting the inherent limitations of prevailing fidelity metrics, including $Fid_+$, $Fid_-$, and $Fid_Δ$. Specifically, a formal, information-theoretic definition of explainability is introduced and it is shown that existing metrics often fail to align with this definition across various statistical scenarios. The reason is due to potential distribution shifts when subgraphs are removed in computing these fidelity measures. Subsequently, a robust class of fidelity measures are introduced, and it is shown analytically that they are resilient to distribution shift issues and are applicable in a wide range of scenarios. Extensive empirical analysis on both synthetic and real datasets are provided to illustrate that the proposed metrics are more coherent with gold standard metrics. The source code is available at https://trustai4s-lab.github.io/fidelity.

Towards Robust Fidelity for Evaluating Explainability of Graph Neural Networks

TL;DR

A formal, information-theoretic definition of explainability is introduced and it is shown that existing metrics often fail to align with this definition across various statistical scenarios, and a robust class of fidelity measures are introduced and it is shown analytically that they are resilient to distribution shift issues and are applicable in a wide range of scenarios.

Abstract

Graph Neural Networks (GNNs) are neural models that leverage the dependency structure in graphical data via message passing among the graph nodes. GNNs have emerged as pivotal architectures in analyzing graph-structured data, and their expansive application in sensitive domains requires a comprehensive understanding of their decision-making processes -- necessitating a framework for GNN explainability. An explanation function for GNNs takes a pre-trained GNN along with a graph as input, to produce a `sufficient statistic' subgraph with respect to the graph label. A main challenge in studying GNN explainability is to provide fidelity measures that evaluate the performance of these explanation functions. This paper studies this foundational challenge, spotlighting the inherent limitations of prevailing fidelity metrics, including , , and . Specifically, a formal, information-theoretic definition of explainability is introduced and it is shown that existing metrics often fail to align with this definition across various statistical scenarios. The reason is due to potential distribution shifts when subgraphs are removed in computing these fidelity measures. Subsequently, a robust class of fidelity measures are introduced, and it is shown analytically that they are resilient to distribution shift issues and are applicable in a wide range of scenarios. Extensive empirical analysis on both synthetic and real datasets are provided to illustrate that the proposed metrics are more coherent with gold standard metrics. The source code is available at https://trustai4s-lab.github.io/fidelity.
Paper Structure (31 sections, 4 theorems, 45 equations, 12 figures, 5 tables, 2 algorithms)

This paper contains 31 sections, 4 theorems, 45 equations, 12 figures, 5 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Information Theoretic Measures for Quantifying Explainability
  4. Fidelity Measures for Explainability
  5. Explainable Tasks vs Explianable Classifiers
  6. Surrogate Fidelity Measures for Quantifying Explainability
  7. The OOD Problem in Evaluating Surrogate Fidelity Measures
  8. A Robust Class of Surrogate Fidelity Measures
  9. Related Work
  10. Experiments
  11. Quantitative Evaluation by Comparing to the Gold Standard
  12. Conclusion
  13. Proofs
  14. Proof of Proposition \ref{['prop:2']}
  15. Proof of Theorem \ref{['th:main:3']}
  16. ...and 16 more sections

Key Result

Theorem 1

Consider a classification task with underlying distribution $P_{Y,{\bm{X}},\mathbf{A}}$, parameters $\zeta,\kappa,\epsilon\in [0,1]$, and an integer $s\in \mathbb{N}$. Then,

Figures (12)

  • Figure 1: Parameter studies on the effects of $\alpha_1$ and $\alpha_2$.
  • Figure 2: Distribution analysis with visualization.
  • Figure 3: KL divergence between down/up-sampled subgraphs and original graphs.
  • Figure 4: Parameter studies on $M$.
  • Figure 5: Fidelity scores with GCN on Tree-Circles. The X-axis value, $\beta_2$ is the ratio of added edges from the non-explanation subgraph to the candidate explanation. The Y-axis value, $\beta_1$ is the ratio of edges removed from ground truth in the candidate explanation.
  • ...and 7 more figures

Theorems & Definitions (13)

  • Definition 1: Classifier
  • Definition 2: Explainable Classification Task
  • Definition 3: Explainable Classifier
  • Theorem 1: Sufficient Conditions for Equivalency of Task and Classifier Explainability
  • Proposition 1: Existence of Accurate and Explainable Classifiers for Explainable Tasks
  • Definition 4: Surrogate Fidelity Measure
  • Definition 5: Rate of Convergence Guarantee
  • Proposition 2: Well-Behavedness of $Fid_{\Delta}$ on Deterministic Tasks
  • Proposition 3: Well-Behavedness of $Fid_{\alpha_1,\alpha_2,\Delta}$ Fidelity Measure
  • proof
  • ...and 3 more