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On Graph Learning with Neural Networks

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Machine Learning, Optimization, and Data Science (LOD 2020)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 12566))

Abstract

Graphs are ideal for modeling natural systems where relations may be intrinsic among data objects. With massive data available, learning graph models from data has become potentially feasible as well as necessary. Yet from the traditional machine learning perspective, learning structural topology of an unknown graphical model remains challenging. In particular, it is computationally intractable to learn graph topologies beyond a tree structure. Nevertheless, deep learning with neural networks, showing great potentials in visual imagery and other application domains, offers an alternative venue for effective machine learning on graphs. In this review, we discuss graph (structure) learning with deep neural networks. In particular, we examine graph neural networks (GNNs) from the task-based and the architecture-based perspectives, respectively.

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References

  1. Atwood, J., Towsley, D.: Diffusion-convolutional neural networks. In: Advances in Neural Information Processing Systems, pp. 1993–2001 (2016)

    Google Scholar 

  2. Bahdanau, D., Cho, K., Bengio, Y.: Neural machine translation by jointly learning to align and translate. arXiv preprint arXiv:1409.0473 (2014)

  3. Bishop, C.M.: Pattern Recognition and Machine Learning. Springer, New York (2006)

    MATH  Google Scholar 

  4. Cai, L., Maffray, F.: On the spanning k-tree problem. Discret. Appl. Math. 44(1–3), 139–156 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  5. Cao, S., Lu, W., Xu, Q.: Deep neural networks for learning graph representations. In: 13th AAAI Conference on Artificial Intelligence (2016)

    Google Scholar 

  6. Chickering, D.M., Geiger, D., Heckerman, D., et al.: Learning Bayesian networks is NP-hard. Technical report. Citeseer (1994)

    Google Scholar 

  7. Chow, C., Liu, C.: Approximating discrete probability distributions with dependence trees. IEEE Trans. Inf. Theor. 14(3), 462–467 (1968)

    Article  MATH  Google Scholar 

  8. Dai, H., Kozareva, Z., Dai, B., Smola, A., Song, L.: Learning steady-states of iterative algorithms over graphs. In: International Conference on Machine Learning, pp. 1106–1114 (2018)

    Google Scholar 

  9. Daly, R., Shen, Q., Aitken, S.: Learning Bayesian networks: approaches and issues. Knowl. Eng. Rev. 26(2), 99 (2011)

    Article  Google Scholar 

  10. De Cao, N., Kipf, T.: MolGAN: an implicit generative model for small molecular graphs. arXiv preprint arXiv:1805.11973 (2018)

  11. Defferrard, M., Bresson, X., Vandergheynst, P.: Convolutional neural networks on graphs with fast localized spectral filtering. In: Advances in Neural Information Processing Systems, pp. 3844–3852 (2016)

    Google Scholar 

  12. Do, K., Tran, T., Venkatesh, S.: Graph transformation policy network for chemical reaction prediction. In: Proceedings of the 25th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining, pp. 750–760 (2019)

    Google Scholar 

  13. Gallicchio, C., Micheli, A.: Graph echo state networks. In: The 2010 International Joint Conference on Neural Networks (IJCNN), pp. 1–8. IEEE (2010)

    Google Scholar 

  14. Ghahramani, Z.: Probabilistic machine learning and artificial intelligence. Nature 521(7553), 452–459 (2015)

    Article  Google Scholar 

  15. Gilmer, J., Schoenholz, S.S., Riley, P.F., Vinyals, O., Dahl, G.E.: Neural message passing for quantum chemistry. In: Proceedings of the 34th International Conference on Machine Learning, vol. 70, pp. 1263–1272. JMLR.org (2017)

    Google Scholar 

  16. Goodfellow, I., Bengio, Y., Courville, A.: Deep Learning. MIT Press, Cambridge (2016)

    MATH  Google Scholar 

  17. Hamilton, W.L., Ying, R., Leskovec, J.: Representation learning on graphs: methods and applications. arXiv preprint arXiv:1709.05584 (2017)

  18. Hassoun, M.H., et al.: Fundamentals of Artificial Neural Networks. MIT Press, Cambridge (1995)

    MATH  Google Scholar 

  19. Jain, A., Zamir, A.R., Savarese, S., Saxena, A.: Structural-RNN: deep learning on spatio-temporal graphs. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 5308–5317 (2016)

    Google Scholar 

  20. Karger, D.R., Srebro, N.: Learning Markov networks: maximum bounded tree-width graphs. In: SODA, pp. 392–401 (2001)

    Google Scholar 

  21. Kipf, T.N., Welling, M.: Semi-supervised classification with graph convolutional networks. arXiv preprint arXiv:1609.02907 (2016)

  22. Kipf, T.N., Welling, M.: Variational graph auto-encoders. arXiv preprint arXiv:1611.07308 (2016)

  23. Koller, D., Friedman, N.: Probabilistic Graphical Models: Principles and Techniques. MIT Press, Cambridge (2009)

    MATH  Google Scholar 

  24. Krizhevsky, A., Sutskever, I., Hinton, G.E.: ImageNet classification with deep convolutional neural networks. In: Advances in Neural Information Processing Systems (NIPS) (2012)

    Google Scholar 

  25. Kullback, S., Leibler, R.A.: On information and sufficiency. Ann. Math. Stat. 22(1), 79–86 (1951)

    Article  MathSciNet  MATH  Google Scholar 

  26. Lauritzen, S.L.: Graphical Models, vol. 17. Clarendon Press, Oxford (1996)

    MATH  Google Scholar 

  27. Lee, J.B., Rossi, R., Kong, X.: Graph classification using structural attention. In: Proceedings of the 24th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining, pp. 1666–1674 (2018)

    Google Scholar 

  28. Lee, J.B., Rossi, R.A., Kim, S., Ahmed, N.K., Koh, E.: Attention models in graphs: a survey. ACM Trans. Knowl. Discov. Data (TKDD) 13(6), 1–25 (2019)

    Article  Google Scholar 

  29. Li, Q., Han, Z., Wu, X.M.: Deeper insights into graph convolutional networks for semi-supervised learning. In: 32nd AAAI Conference on Artificial Intelligence (2018)

    Google Scholar 

  30. Li, R., Wang, S., Zhu, F., Huang, J.: Adaptive graph convolutional neural networks. In: 32nd AAAI Conference on Artificial Intelligence (2018)

    Google Scholar 

  31. Li, Y., Yu, R., Shahabi, C., Liu, Y.: Diffusion convolutional recurrent neural network: data-driven traffic forecasting. arXiv preprint arXiv:1707.01926 (2017)

  32. Li, Y., Tarlow, D., Brockschmidt, M., Zemel, R.: Gated graph sequence neural networks. arXiv preprint arXiv:1511.05493 (2015)

  33. Ma, T., Chen, J., Xiao, C.: Constrained generation of semantically valid graphs via regularizing variational autoencoders. In: Advances in Neural Information Processing Systems, pp. 7113–7124 (2018)

    Google Scholar 

  34. Mandic, D., Chambers, J.: Recurrent Neural Networks for Prediction: Learning Algorithms, Architectures and Stability. Wiley, Hoboken (2001)

    Book  Google Scholar 

  35. Micheli, A.: Neural network for graphs: a contextual constructive approach. IEEE Trans. Neural Netw. 20(3), 498–511 (2009)

    Article  MathSciNet  Google Scholar 

  36. Monti, F., Boscaini, D., Masci, J., Rodola, E., Svoboda, J., Bronstein, M.M.: Geometric deep learning on graphs and manifolds using mixture model CNNs. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 5115–5124 (2017)

    Google Scholar 

  37. Nair, V., Hinton, G.E.: Rectified linear units improve restricted Boltzmann machines. In: International Conference on Machine Learning (ICML) (2010)

    Google Scholar 

  38. Niepert, M., Ahmed, M., Kutzkov, K.: Learning convolutional neural networks for graphs. In: International Conference on Machine Learning, pp. 2014–2023 (2016)

    Google Scholar 

  39. Pan, S., Hu, R., Long, G., Jiang, J., Yao, L., Zhang, C.: Adversarially regularized graph autoencoder for graph embedding. arXiv preprint arXiv:1802.04407 (2018)

  40. Pan, S., Wu, J., Zhu, X., Long, G., Zhang, C.: Task sensitive feature exploration and learning for multitask graph classification. IEEE Tran. Cybern. 47(3), 744–758 (2016)

    Article  Google Scholar 

  41. Pan, S., Wu, J., Zhu, X., Zhang, C., Philip, S.Y.: Joint structure feature exploration and regularization for multi-task graph classification. IEEE Trans. Knowl. Data Eng. 28(3), 715–728 (2015)

    Article  Google Scholar 

  42. Scarselli, F., Gori, M., Tsoi, A.C., Hagenbuchner, M., Monfardini, G.: The graph neural network model. IEEE Trans. Neural Netw. 20(1), 61–80 (2008)

    Article  Google Scholar 

  43. Teyssier, M., Koller, D.: Ordering-based search: a simple and effective algorithm for learning Bayesian networks. arXiv preprint arXiv:1207.1429 (2012)

  44. Tu, K., Cui, P., Wang, X., Yu, P.S., Zhu, W.: Deep recursive network embedding with regular equivalence. In: Proceedings of the 24th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining, pp. 2357–2366 (2018)

    Google Scholar 

  45. Veličković, P., Cucurull, G., Casanova, A., Romero, A., Lio, P., Bengio, Y.: Graph attention networks. arXiv preprint arXiv:1710.10903 (2017)

  46. Wu, Z., Pan, S., Chen, F., Long, G., Zhang, C., Philip, S.Y.: A comprehensive survey on graph neural networks. IEEE Trans. Neural Netw. Learn. Syst., 1–21 (2020)

    Google Scholar 

  47. Yan, S., Xiong, Y., Lin, D.: Spatial temporal graph convolutional networks for skeleton-based action recognition. In: 32nd AAAI Conference on Artificial Intelligence (2018)

    Google Scholar 

  48. Ying, Z., You, J., Morris, C., Ren, X., Hamilton, W., Leskovec, J.: Hierarchical graph representation learning with differentiable pooling. In: Advances in Neural Information Processing Systems, pp. 4800–4810 (2018)

    Google Scholar 

  49. You, J., Liu, B., Ying, Z., Pande, V., Leskovec, J.: Graph convolutional policy network for goal-directed molecular graph generation. In: Advances in Neural Information Processing Systems, pp. 6410–6421 (2018)

    Google Scholar 

  50. You, J., Ying, R., Ren, X., Hamilton, W.L., Leskovec, J.: GraphRNN: generating realistic graphs with deep auto-regressive models. arXiv preprint arXiv:1802.08773 (2018)

  51. Yuan, C., Malone, B.: Learning optimal Bayesian networks: a shortest path perspective. J. Artif. Intell. Res. 48, 23–65 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  52. Zhang, M., Cui, Z., Neumann, M., Chen, Y.: An end-to-end deep learning architecture for graph classification. In: 32nd AAAI Conference on Artificial Intelligence (2018)

    Google Scholar 

  53. Zhang, Z., Cui, P., Zhu, W.: Deep learning on graphs: a survey. IEEET Trans. Knowl. Data Eng. (2020)

    Google Scholar 

  54. Zhou, J., et al.: Graph neural networks: a review of methods and applications. arXiv preprint arXiv:1812.08434 (2018)

  55. Zhuang, C., Ma, Q.: Dual graph convolutional networks for graph-based semi-supervised classification. In: Proceedings of the 2018 World Wide Web Conference, pp. 499–508 (2018)

    Google Scholar 

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Correspondence to Zahra Jandaghi .

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Jandaghi, Z., Cai, L. (2020). On Graph Learning with Neural Networks. In: Nicosia, G., et al. Machine Learning, Optimization, and Data Science. LOD 2020. Lecture Notes in Computer Science(), vol 12566. Springer, Cham. https://doi.org/10.1007/978-3-030-64580-9_43

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  • DOI: https://doi.org/10.1007/978-3-030-64580-9_43

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-64579-3

  • Online ISBN: 978-3-030-64580-9

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