Yifei Liu
ABSTRACT
Probabilistic graphical models, such as Markov random fields (MRF), exploit dependencies among random variables to model a rich family of joint probability distributions. Inference algorithms, such as belief propagation (BP), can effectively compute the marginal posteriors for decision making. Nonetheless, inferences involve sophisticated probability calculations and are difficult for humans to interpret. Among all existing explanation methods for MRFs, no method is designed for fair attributions of an inference outcome to elements on the MRF where the inference takes place. Shapley values provide rigorous attributions but so far have not been studied on MRFs. We thus define Shapley values for MRFs to capture both probabilistic and topological contributions of the variables on MRFs. We theoretically characterize the new definition regarding independence, equal contribution, additivity, and submodularity. As brute-force computation of the Shapley values is challenging, we propose GraphShapley, an approximation algorithm that exploits the decomposability of Shapley values, the structure of MRFs, and the iterative nature of BP inference to speed up the computation. In practice, we propose meta-explanations to explain the Shapley values and make them more accessible and trustworthy to human users. On four synthetic and nine real-world MRFs, we demonstrate that GraphShapley generates sensible and practical explanations.
Supplemental Material
- Julius Adebayo, Justin Gilmer, Michael Muelly, Ian Goodfellow, Moritz Hardt, and Been Kim. 2018. Sanity Checks for Saliency Maps. In NeurIPS.Google Scholar
- Marco Ancona, Cengiz Oztireli, and Markus Gross. 2019. Explaining Deep Neural Networks with a Polynomial Time Algorithm for Shapley Values Approximation. In ICML.Google Scholar
- Javier Castro, Daniel Gó mez, and Juan Tejada. 2009. Polynomial calculation of the Shapley value based on sampling. Computers & Operations Research, Vol. 36, 5 (2009), 1726--1730.Google ScholarDigital Library
- Hei Chan and Adnan Darwiche. 2005. Sensitivity analysis in Markov networks. In IJCAI.Google Scholar
- Chao Chen, Yifei Liu, Xi Zhang, and Sihong Xie. 2019 a. Scalable Explanation of Inferences on Large Graphs. In ICDM.Google Scholar
- Jianbo Chen, Le Song, Martin J. Wainwrightand, and Michael I. Jordan. 2019 b. L-shapley and c-shapley: Efficient model interpretation for structured data. In ICLR.Google Scholar
- Adnan Darwiche. 2003. A differential approach to inference in Bayesian networks. Journal of the ACM (JACM) (2003), 280--305.Google Scholar
- Mengnan Du, Ninghao Liu, and Xia Hu. 2019. Techniques for Interpretable Machine Learning. Commun. ACM, Vol. 63, 1 (2019), 68--77.Google ScholarDigital Library
- Papachristoudis Georgios and Fisher III John. 2015. Adaptive Belief Propagation. In ICML.Google Scholar
- Amirata Ghorbani, Abubakar Abid, and James Y Zou. 2017. Interpretation of Neural Networks is Fragile. In AAAI.Google Scholar
- Amirata Ghorbani and James Zou. 2019. Data Shapley: Equitable Valuation of Data for Machine Learning. In ICML.Google Scholar
- L H Gilpin, D Bau, B Z Yuan, A Bajwa, M Specter, and L Kagal. 2018. Explaining Explanations: An Overview of Interpretability of Machine Learning. In DSAA. 80--89.Google Scholar
- Riccardo Guidotti, Anna Monreale, Franco Turini, Dino Pedreschi, and Fosca Giannotti. 2018. A Survey of Methods for Explaining Black Box Models. ACM Comput. Surv., Vol. 51 (2018), 93:1--93:42.Google ScholarDigital Library
- Qiang Huang, Makoto Yamada, Yuan Tian, Dinesh Singh, Dawei Yin, and Yi Chang. 2020. GraphLIME: Local Interpretable Model Explanations for Graph Neural Networks. (2020).Google Scholar
- Sarthak Jain and Byron C Wallace. 2019. A ttention is not E xplanation. In NAACL.Google Scholar
- K. Jha, Y. Wang, G. Xun, and A. Zhang. 2018. Interpretable Word Embeddings for Medical Domain. In ICDM.Google Scholar
- Ruoxi Jia, David Dao, Boxin Wang, Frances Ann Hubis, Nick Hynes, Nezihe Merve Gurel, Bo Li, Ce Zhang, Dawn Song, and Costas Spanos. 2019. Towards Efficient Data Valuation Based on the Shapley Value. In AISTATS. 1167--1176.Google Scholar
- Murphy Kevin. 2001 (accessed April 25, 2020). List of Bayesian Network Software. https://www.cs.ubc.ca/murphyk/Bayes/old.bnsoft.htmlGoogle Scholar
- Daphne Koller and Nir Friedman. 2009. Probabilistic graphical model: principles and techniques .MIT Press.Google Scholar
- Andrew McCallum, Dayne Freitag, and Fernando C. N. Pereira. 2000. Maximum Entropy Markov Models for Information Extraction and Segmentation. In ICML.Google ScholarDigital Library
- Tomasz P. Michalak, Karthik .V. Aadithya, Piotr L. Szczepa'ski, Balaraman Ravindran, and Nicholas R. Jennings. 2013. Effcient Computation of the Shapley Value for Game-Theoretic Network Centrality. JAIR, Vol. 46 (2013), 607--650.Google ScholarCross Ref
- Tim Miller. 2019. Explanation in artificial intelligence: Insights from the social sciences. Artificial Intelligence, Vol. 267 (2019), 1--38.Google ScholarCross Ref
- Brent Mittelstadt, Chris Russell, and Sandra Wachter. 2019. Explaining Explanations in AI. In Proceedings of the Conference on Fairness, Accountability, and Transparency.Google ScholarDigital Library
- Galileo Mark Namata, Ben London, and Lise Getoor. 2016. Collective graph identification. ACM TKDD, Vol. 10, 3 (2016), 25.Google Scholar
- G. L. Nemhauser, L. A. Wolsey, and M. L. Fisher. 1978. An analysis of approximations for maximizing submodular set functions. Mathematical Programming, Vol. 14, 1 (Dec 1978), 265--294.Google ScholarDigital Library
- Lawrence Page, Sergey Brin, Rajeev Motwani, and Terry Winograd. 1999. The PageRank citation ranking: Bringing order to the web. Technical Report. Stanford InfoLab.Google Scholar
- Shashank Pandit, Duen Horng Chau, Samuel Wang, and Christos Faloutsos. 2007. Netprobe: A Fast and Scalable System for Fraud Detection in Online Auction Networks. In WWW.Google Scholar
- Bryan Perozzi, Rami Al-Rfou, and Steven Skiena. 2014. Deepwalk: Online learning of social representations. In SIGKDD.Google ScholarDigital Library
- Forough Poursabzi-Sangdeh, Dan Goldstein, Jake Hofman, Jennifer Wortman Vaughan, and Hanna Wallach. 2018. Manipulating and Measuring Model Interpretability.Google Scholar
- Danish Pruthi, Mansi Gupta, Bhuwan Dhingra, Graham Neubig, and Zachary Chase Lipton. 2019. Learning to Deceive with Attention-Based Explanations. ArXiv, Vol. abs/1909.0 (2019).Google Scholar
- Shebuti Rayana and Leman Akoglu. 2015. Collective opinion spam detection: Bridging review networks and metadata. In SIGKDD.Google Scholar
- Marco Tulio Ribeiro, Sameer Singh, and Carlos Guestrin. 2016. Why should i trust you?: Explaining the predictions of any classifier. In SIGKDD.Google Scholar
- Andrew Slavin Ross, Michael C Hughes, and Finale Doshi-Velez. 2017. Right for the Right Reasons: Training Differentiable Models by Constraining their Explanations. In IJCAI.Google Scholar
- L Shapley. 1953. A Value for n-Person Games. Contributions to the Theory of Games (1953), 31--40.Google Scholar
- Avanti Shrikumar, Peyton Greenside, and Anshul Kundaje. 2017. Learning Important Features Through Propagating Activation Differences. In ICML.Google Scholar
- Oskar Skibski, Talal Rahwan, Tomasz P. Michalak, and Michael Wooldridge. 2019. Enumerating Connected Subgraphs and Computing the Myerson and Shapley Values in Graph-Restricted Games. ACM TIST, Vol. 10, 2 (2019), 15.Google Scholar
- Erik Strumbelj and Igor Kononenko. 2010. An Efficient Explanation of Individual Classifications using Game Theory. JMLR (2010).Google Scholar
- Erik vS trumbelj and Igor Kononenko. 2014. Explaining prediction models and individual predictions with feature contributions. Knowledge and Information Systems, Vol. 41, 3 (2014), 647--665.Google ScholarDigital Library
- Henri Jacques Suermondt. 1992. Explanation in Bayesian Belief Networks. Ph.D. Dissertation.Google Scholar
- Mukund Sundararajan, Ankur Taly, and Qiqi Yan. 2017. Axiomatic Attribution for Deep Networks. In ICML.Google Scholar
- Lei Tang and Huan Liu. 2009. Relational learning via latent social dimensions. In SIGKDD.Google Scholar
- Jeroen Van Bouwel and Erik Weber. 2002. Remote Causes, Bad Explanations? Journal for the Theory of Social Behaviour, Vol. 32, 4 (2002), 437--449.Google ScholarCross Ref
- Xifeng Yan and Jiawei Han. 2002. gspan: Graph-based substructure pattern mining. In ICDM.Google Scholar
- Chih-Kuan Yeh, Cheng-Yu Hsieh, Arun Sai Suggala, David W Inouye, and Pradeep D Ravikumar. 2019. On the (In)fidelity and Sensitivity of Explanations. In NeurIPS.Google Scholar
- Ming Yin, Jennifer Wortman Vaughan, and Hanna Wallach. 2019. Understanding the Effect of Accuracy on Trust in Machine Learning Models (CHI).Google ScholarDigital Library
- Rex Ying, Dylan Bourgeois, Jiaxuan You, Marinka Zitnik, and Jure Leskovec. 2019. GNN Explainer: A Tool for Post-hoc Explanation of Graph Neural Networks. In NeurIPS.Google Scholar
- KiJung Yoon, Renjie Liao, Yuwen Xiong, Lisa Zhang, Ethan Fetaya, Raquel Urtasun, Richard Zemel, and Xaq Pitkow. 2018. Inference in probabilistic graphical models by graph neural networks. In ICLR workshop.Google Scholar
- Xinyang Zhang, Ningfei Wang, Shouling Ji, Hua Shen, and Ting Wang. 2018. Interpretable Deep Learning under Fire. ArXiv, Vol. abs/1812.0 (2018).Google Scholar
Index Terms
- Shapley Values and Meta-Explanations for Probabilistic Graphical Model Inference
Recommendations
Explanations for Data Repair Through Shapley Values
CIKM '21: Proceedings of the 30th ACM International Conference on Information & Knowledge ManagementData repair, i.e., the identification and fix of errors in the data, is a central component of the Data Science cycle. As such, significant research effort has been devoted to automate the repair process. Yet it still requires significant manual labor ...
Learning Graphical Model Parameters with Approximate Marginal Inference
Likelihood-based learning of graphical models faces challenges of computational complexity and robustness to model misspecification. This paper studies methods that fit parameters directly to maximize a measure of the accuracy of predicted marginals, ...
An Introduction to Variational Methods for Graphical Models
This paper presents a tutorial introduction to the use of variational methods for inference and learning in graphical models (Bayesian networks and Markov random fields). We present a number of examples of graphical models, including the QMR-DT database, ...
Comments