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# PGM-Explainer: Probabilistic Graphical Model Explanations for Graph Neural Networks

NIPS 2020, (2020)

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Abstract

In Graph Neural Networks (GNNs), the graph structure is incorporated into the learning of node representations. This complex structure makes explaining GNNs' predictions become much more challenging. In this paper, we propose PGM-Explainer, a Probabilistic Graphical Model (PGM) model-agnostic explainer for GNNs. Given a prediction to be...More

Introduction

- Graph Neural Networks (GNNs) have been emerging as powerful solutions to many real-world applications in various domains where the datasets are in form of graphs such as social networks, citation networks, knowledge graphs, and biological networks [1, 2, 3].
- (b) Knowledge on model’s behaviors helps them identify scenarios in which the systems may fail.
- As the field grows, understanding why GNNs made such decisions becomes more vital.
- This is essential for safety reason in complex real-world tasks in which not all possible scenarios are testable.
- Understanding the model’s decisions helps them discover these biases before its deployment

Highlights

- Graph Neural Networks (GNNs) have been emerging as powerful solutions to many real-world applications in various domains where the datasets are in form of graphs such as social networks, citation networks, knowledge graphs, and biological networks [1, 2, 3]
- Our results show that Probabilistic Graphical Model (PGM)-Explainer achieves significantly higher precision than other methods in these experiments
- We propose PGM-Explainer, an explanation method faithfully explaining the predictions of any GNN in an interpretable manner
- By approximating the target prediction with a graphical model, PGM-Explainer is able to demonstrate the non-linear contributions of explained features toward the prediction
- Our experiments show the high accuracy and precision of PGMExplainer and imply that PGM explanations are favored by end-users
- We only adopt Bayesian networks as interpretable models, our formulations of PGM-Explainer supports the exploration of others graphical models such as Markov networks and Dependency networks

Methods

- The authors provide the experiments, comparing the performance of PGM-Explainer to that of existing explanation methods for GNNs, including GNNExplainer [24] and the implementation of the extension of SHapley Additive exPlanations (SHAP) [17] to GNNs.
- Source codes of gradient-based methods for GNNs are either unavailable or limited to specific models/applications.
- SHAP is an additive feature attribution methods, unifying explanation methods for conventional neural networks [17].
- By comparing PGM-Explainer with SHAP, the authors aim to demonstrate drawbacks of the linear-independence assumption of explained features in explaining GNN’s predictions.
- The authors show that the vanilla gradient-based explanation method and GNNExplainer can be considered as additive feature attribution methods in Appendix A.
- The authors' source code can be found at [34]

Results

**Results on Synthetic Datasets**

Table 2 shows the accuracy in the explanations generated by different explainers.- The explanations are generated for all nodes in the motifs of the input graph.
- The precision of nodes in explanations of each explainer on Trust weighted signed networks datasets are reported in Table 3.
- The authors compare PGM-Explainer with the SHAP extension for GNN and GRAD, a simple gradient approach.
- In this experiment, the authors do not restrict the number of nodes returned by PGM-Explainer.
- In GRAD, the top-3 nodes are chosen based on the sum gradients of the GNN’s loss function with respect to the associated node features

Conclusion

- The authors propose PGM-Explainer, an explanation method faithfully explaining the predictions of any GNN in an interpretable manner.
- By approximating the target prediction with a graphical model, PGM-Explainer is able to demonstrate the non-linear contributions of explained features toward the prediction.
- The authors only adopt Bayesian networks as interpretable models, the formulations of PGM-Explainer supports the exploration of others graphical models such as Markov networks and Dependency networks.

Summary

## Introduction:

Graph Neural Networks (GNNs) have been emerging as powerful solutions to many real-world applications in various domains where the datasets are in form of graphs such as social networks, citation networks, knowledge graphs, and biological networks [1, 2, 3].- (b) Knowledge on model’s behaviors helps them identify scenarios in which the systems may fail.
- As the field grows, understanding why GNNs made such decisions becomes more vital.
- This is essential for safety reason in complex real-world tasks in which not all possible scenarios are testable.
- Understanding the model’s decisions helps them discover these biases before its deployment
## Objectives:

The authors aim to explain the prediction of the role of node E. (c) A PGMexplanation in a form of Bayesian network.- The authors aim to explain the prediction of the role of node E.
- (c) A PGMexplanation in a form of Bayesian network.
- By comparing PGM-Explainer with SHAP, the authors aim to demonstrate drawbacks of the linear-independence assumption of explained features in explaining GNN’s predictions.
- The authors' aim is to bring a clearer view on explanation models and show that the class of additive feature attribution methods introduced in [17] fully captures current explanation methods for GNNs. The authors aim to find a graph, called perfect map, that precisely capture P
## Methods:

The authors provide the experiments, comparing the performance of PGM-Explainer to that of existing explanation methods for GNNs, including GNNExplainer [24] and the implementation of the extension of SHapley Additive exPlanations (SHAP) [17] to GNNs.- Source codes of gradient-based methods for GNNs are either unavailable or limited to specific models/applications.
- SHAP is an additive feature attribution methods, unifying explanation methods for conventional neural networks [17].
- By comparing PGM-Explainer with SHAP, the authors aim to demonstrate drawbacks of the linear-independence assumption of explained features in explaining GNN’s predictions.
- The authors show that the vanilla gradient-based explanation method and GNNExplainer can be considered as additive feature attribution methods in Appendix A.
- The authors' source code can be found at [34]
## Results:

**Results on Synthetic Datasets**

Table 2 shows the accuracy in the explanations generated by different explainers.- The explanations are generated for all nodes in the motifs of the input graph.
- The precision of nodes in explanations of each explainer on Trust weighted signed networks datasets are reported in Table 3.
- The authors compare PGM-Explainer with the SHAP extension for GNN and GRAD, a simple gradient approach.
- In this experiment, the authors do not restrict the number of nodes returned by PGM-Explainer.
- In GRAD, the top-3 nodes are chosen based on the sum gradients of the GNN’s loss function with respect to the associated node features
## Conclusion:

The authors propose PGM-Explainer, an explanation method faithfully explaining the predictions of any GNN in an interpretable manner.- By approximating the target prediction with a graphical model, PGM-Explainer is able to demonstrate the non-linear contributions of explained features toward the prediction.
- The authors only adopt Bayesian networks as interpretable models, the formulations of PGM-Explainer supports the exploration of others graphical models such as Markov networks and Dependency networks.

- Table1: Models’ accuracy and number of sampled data used by PGM-Explainer
- Table2: Accuracy of Explainers on Synthetic Datasets
- Table3: Precision of Explainers on Trust Signed networks datasets
- Table4: Parameters of synthetic datasets

Funding

- Acknowledgments and Disclosure of Funding This work was supported in part by the National Science Foundation Program on Fairness in AI in collaboration with Amazon under award No 1939725

Study subjects and analysis

synthetic datasets: 6

Synthetic node classification task. Six synthetic datasets, detailed in Appendix I, were considered. We reuse the source code of [24] as we want to evaluate explainers on the same settings

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- 2. All structure B such that I(B) = I(B∗) will have strictly lower score.

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