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

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 explained, PGM-Explainer identifies crucial graph components and generates an explanation in form of a PGM approximating that prediction. Different from existing explainers for GNNs where the explanations are drawn from a set of linear functions of explained features, PGM-Explainer is able to demonstrate the dependencies of explained features in form of conditional probabilities. Our theoretical analysis shows that the PGM generated by PGM-Explainer includes the Markov-blanket of the target prediction, i.e. including all its statistical information. We also show that the explanation returned by PGM-Explainer contains the same set of independence statements in the perfect map. Our experiments on both synthetic and real-world datasets show that PGM-Explainer achieves better performance than existing explainers in many benchmark tasks.

[1]  Ankur Taly,et al.  Gradients of Counterfactuals , 2016, ArXiv.

[2]  Abhishek Das,et al.  Grad-CAM: Visual Explanations from Deep Networks via Gradient-Based Localization , 2016, 2017 IEEE International Conference on Computer Vision (ICCV).

[3]  Jaewoo Kang,et al.  Self-Attention Graph Pooling , 2019, ICML.

[4]  Alexander Binder,et al.  On Pixel-Wise Explanations for Non-Linear Classifier Decisions by Layer-Wise Relevance Propagation , 2015, PloS one.

[5]  Fabio Stella,et al.  A survey on Bayesian network structure learning from data , 2019, Progress in Artificial Intelligence.

[6]  Max Welling,et al.  Semi-Supervised Classification with Graph Convolutional Networks , 2016, ICLR.

[7]  My T. Thai,et al.  Evaluating Explainers via Perturbation , 2019, ArXiv.

[8]  Alexander J. Smola,et al.  Deep Graph Library: Towards Efficient and Scalable Deep Learning on Graphs , 2019, ArXiv.

[9]  Avanti Shrikumar,et al.  Learning Important Features Through Propagating Activation Differences , 2017, ICML.

[10]  Nir Friedman,et al.  Probabilistic Graphical Models: Principles and Techniques - Adaptive Computation and Machine Learning , 2009 .

[11]  Jure Leskovec,et al.  Inductive Representation Learning on Large Graphs , 2017, NIPS.

[12]  Lihui Chen,et al.  Capsule Graph Neural Network , 2018, ICLR.

[13]  Carlos Guestrin,et al.  "Why Should I Trust You?": Explaining the Predictions of Any Classifier , 2016, ArXiv.

[14]  Heiko Hoffmann,et al.  Explainability Methods for Graph Convolutional Neural Networks , 2019, 2019 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR).

[15]  Xavier Bresson,et al.  Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering , 2016, NIPS.

[16]  Yixin Chen,et al.  Link Prediction Based on Graph Neural Networks , 2018, NeurIPS.

[17]  Natalia Gimelshein,et al.  PyTorch: An Imperative Style, High-Performance Deep Learning Library , 2019, NeurIPS.

[18]  Jose Miguel Puerta,et al.  Learning Bayesian networks by hill climbing: efficient methods based on progressive restriction of the neighborhood , 2010, Data Mining and Knowledge Discovery.

[19]  Xavier Bresson,et al.  CayleyNets: Graph Convolutional Neural Networks With Complex Rational Spectral Filters , 2017, IEEE Transactions on Signal Processing.

[20]  Jure Leskovec,et al.  GNNExplainer: Generating Explanations for Graph Neural Networks , 2019, NeurIPS.

[21]  Jure Leskovec,et al.  Graph Convolutional Policy Network for Goal-Directed Molecular Graph Generation , 2018, NeurIPS.

[22]  Andrew Zisserman,et al.  Deep Inside Convolutional Networks: Visualising Image Classification Models and Saliency Maps , 2013, ICLR.

[23]  Sebastian Thrun,et al.  Bayesian Network Induction via Local Neighborhoods , 1999, NIPS.

[24]  Thomas Brox,et al.  Striving for Simplicity: The All Convolutional Net , 2014, ICLR.

[25]  Albert-Lszl Barabsi,et al.  Network Science , 2016, Encyclopedia of Big Data.

[26]  Christos Faloutsos,et al.  Edge Weight Prediction in Weighted Signed Networks , 2016, 2016 IEEE 16th International Conference on Data Mining (ICDM).

[27]  Jure Leskovec,et al.  Hierarchical Graph Representation Learning with Differentiable Pooling , 2018, NeurIPS.

[28]  Michael M. Bronstein,et al.  MOTIFNET: A MOTIF-BASED GRAPH CONVOLUTIONAL NETWORK FOR DIRECTED GRAPHS , 2018, 2018 IEEE Data Science Workshop (DSW).

[29]  Scott Lundberg,et al.  A Unified Approach to Interpreting Model Predictions , 2017, NIPS.

[30]  Jimmy Ba,et al.  Adam: A Method for Stochastic Optimization , 2014, ICLR.

[31]  Judea Pearl,et al.  MARKOV AND BAYESIAN NETWORKS: Two Graphical Representations of Probabilistic Knowledge , 1988 .

[32]  Zhe L. Lin,et al.  Top-Down Neural Attention by Excitation Backprop , 2016, International Journal of Computer Vision.

[33]  Been Kim,et al.  Towards A Rigorous Science of Interpretable Machine Learning , 2017, 1702.08608.

[34]  Yoshua Bengio,et al.  Benchmarking Graph Neural Networks , 2023, J. Mach. Learn. Res..

[35]  Pietro Liò,et al.  Graph Attention Networks , 2017, ICLR.

[36]  Jure Leskovec,et al.  Modeling polypharmacy side effects with graph convolutional networks , 2018, bioRxiv.

[37]  Jure Leskovec,et al.  How Powerful are Graph Neural Networks? , 2018, ICLR.