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Verifying Relational Explanations: A Probabilistic Approach

Abisha Thapa Magar, Anup Shakya, Somdeb Sarkhel, Deepak Venugopal

TL;DR

The paper tackles the challenge of verifying relational explanations produced by graph neural networks, which are difficult to assess with human judgments due to their graph-structured nature. It introduces a probabilistic verification framework that constructs a distribution over symmetric counterfactual explanations via Boolean matrix factorization, encodes this distribution in a factor graph, and uses Belief Propagation to quantify uncertainty in explanations. By incorporating GNNExplainer explanations as weighted factors, the method measures how much an explanation reduces uncertainty, evaluated through McNemar’s test on several benchmark datasets. Results indicate that the proposed BP-based uncertainty estimates are statistically more reliable than those directly provided by GNNExplainer, particularly on more complex relational graphs. The approach offers a scalable, principled way to verify relational explanations and could be extended with user feedback in future work.

Abstract

Explanations on relational data are hard to verify since the explanation structures are more complex (e.g. graphs). To verify interpretable explanations (e.g. explanations of predictions made in images, text, etc.), typically human subjects are used since it does not necessarily require a lot of expertise. However, to verify the quality of a relational explanation requires expertise and is hard to scale-up. GNNExplainer is arguably one of the most popular explanation methods for Graph Neural Networks. In this paper, we develop an approach where we assess the uncertainty in explanations generated by GNNExplainer. Specifically, we ask the explainer to generate explanations for several counterfactual examples. We generate these examples as symmetric approximations of the relational structure in the original data. From these explanations, we learn a factor graph model to quantify uncertainty in an explanation. Our results on several datasets show that our approach can help verify explanations from GNNExplainer by reliably estimating the uncertainty of a relation specified in the explanation.

Verifying Relational Explanations: A Probabilistic Approach

TL;DR

The paper tackles the challenge of verifying relational explanations produced by graph neural networks, which are difficult to assess with human judgments due to their graph-structured nature. It introduces a probabilistic verification framework that constructs a distribution over symmetric counterfactual explanations via Boolean matrix factorization, encodes this distribution in a factor graph, and uses Belief Propagation to quantify uncertainty in explanations. By incorporating GNNExplainer explanations as weighted factors, the method measures how much an explanation reduces uncertainty, evaluated through McNemar’s test on several benchmark datasets. Results indicate that the proposed BP-based uncertainty estimates are statistically more reliable than those directly provided by GNNExplainer, particularly on more complex relational graphs. The approach offers a scalable, principled way to verify relational explanations and could be extended with user feedback in future work.

Abstract

Explanations on relational data are hard to verify since the explanation structures are more complex (e.g. graphs). To verify interpretable explanations (e.g. explanations of predictions made in images, text, etc.), typically human subjects are used since it does not necessarily require a lot of expertise. However, to verify the quality of a relational explanation requires expertise and is hard to scale-up. GNNExplainer is arguably one of the most popular explanation methods for Graph Neural Networks. In this paper, we develop an approach where we assess the uncertainty in explanations generated by GNNExplainer. Specifically, we ask the explainer to generate explanations for several counterfactual examples. We generate these examples as symmetric approximations of the relational structure in the original data. From these explanations, we learn a factor graph model to quantify uncertainty in an explanation. Our results on several datasets show that our approach can help verify explanations from GNNExplainer by reliably estimating the uncertainty of a relation specified in the explanation.
Paper Structure (16 sections, 11 equations, 4 figures, 1 algorithm)

This paper contains 16 sections, 11 equations, 4 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Work
  3. Background
  4. Graph Convolutional Networks
  5. GNNExplainer
  6. Verification of Explanations
  7. Counterfactual Relational Explanations
  8. Boolean Factorization
  9. Factor Graph Model
  10. Uncertainty Estimation
  11. Experiments
  12. Evaluation Procedure
  13. Setup
  14. Datasets
  15. Results
  16. ...and 1 more sections

Figures (4)

  • Figure 1: Given the original graph (the first one), different symmetric approximations of the original graph are shown.
  • Figure 2: (a) shows the original factor graph, (b) shows the added factor based on a new explanation $x_1,x_3$ with confidence $GC$ (c) shows the difference in joint probabilities $p(x_1,x_3)$ before and after the factor is added for different values of $GC$.
  • Figure 3: Results from McNemar's test to verify uncertainty quantification in benchmarks.
  • Figure 4: Results from McNemar's test to verify uncertainty quantification in benchmarks.

Theorems & Definitions (3)

  • Definition 1
  • Definition 2
  • Definition 3