Contextual Graph Markov Model: A Deep and Generative Approach to Graph Processing

We introduce the Contextual Graph Markov Model, an approach combining ideas from generative models and neural networks for the processing of graph data. It founds on a constructive methodology to build a deep architecture comprising layers of probabilistic models that learn to encode the structured information in an incremental fashion. Context is diffused in an efficient and scalable way across the graph vertexes and edges. The resulting graph encoding is used in combination with discriminative models to address structure classification benchmarks.

[1]  Christian Lebiere,et al.  The Cascade-Correlation Learning Architecture , 1989, NIPS.

[2]  A. Debnath,et al.  Structure-activity relationship of mutagenic aromatic and heteroaromatic nitro compounds. Correlation with molecular orbital energies and hydrophobicity. , 1991, Journal of medicinal chemistry.

[3]  Alessandro Sperduti,et al.  A general framework for adaptive processing of data structures , 1998, IEEE Trans. Neural Networks.

[4]  Alexander J. Smola,et al.  Fast Kernels for String and Tree Matching , 2002, NIPS.

[5]  Michael Collins,et al.  New Ranking Algorithms for Parsing and Tagging: Kernels over Discrete Structures, and the Voted Perceptron , 2002, ACL.

[6]  Hisashi Kashima,et al.  Marginalized Kernels Between Labeled Graphs , 2003, ICML.

[7]  Paolo Frasconi,et al.  Hidden Tree Markov Models for Document Image Classification , 2003, IEEE Trans. Pattern Anal. Mach. Intell..

[8]  Luc De Raedt,et al.  Data Mining and Machine Learning Techniques for the Identification of Mutagenicity Inducing Substructures and Structure Activity Relationships of Noncongeneric Compounds , 2004, J. Chem. Inf. Model..

[9]  Hans-Peter Kriegel,et al.  Shortest-path kernels on graphs , 2005, Fifth IEEE International Conference on Data Mining (ICDM'05).

[10]  Luc De Raedt,et al.  Don't Be Afraid of Simpler Patterns , 2006, PKDD.

[11]  Alessandro Moschitti,et al.  Efficient Convolution Kernels for Dependency and Constituent Syntactic Trees , 2006, ECML.

[12]  Ludovic Denoyer,et al.  Report on the XML mining track at INEX 2005 and INEX 2006: categorization and clustering of XML documents , 2007, SIGF.

[13]  Sebastian Nowozin,et al.  gBoost: a mathematical programming approach to graph classification and regression , 2009, Machine Learning.

[14]  Karsten M. Borgwardt,et al.  Fast subtree kernels on graphs , 2009, NIPS.

[15]  Ah Chung Tsoi,et al.  The Graph Neural Network Model , 2009, IEEE Transactions on Neural Networks.

[16]  Alessio Micheli,et al.  Neural Network for Graphs: A Contextual Constructive Approach , 2009, IEEE Transactions on Neural Networks.

[17]  Alessandro Sperduti,et al.  A Tree-Based Kernel for Graphs , 2012, SDM.

[18]  Davide Bacciu,et al.  A Generative Multiset Kernel for Structured Data , 2012, ICANN.

[19]  Davide Bacciu,et al.  Compositional Generative Mapping for Tree-Structured Data—Part I: Bottom-Up Probabilistic Modeling of Trees , 2012, IEEE Transactions on Neural Networks and Learning Systems.

[20]  Davide Bacciu,et al.  An input-output hidden Markov model for tree transductions , 2013, Neurocomputing.

[21]  Claudio Gallicchio,et al.  Tree Echo State Networks , 2013, Neurocomputing.

[22]  Davide Bacciu,et al.  Modeling Bi-directional Tree Contexts by Generative Transductions , 2014, ICONIP.

[23]  Alessandro Sperduti,et al.  Graph Kernels Exploiting Weisfeiler-Lehman Graph Isomorphism Test Extensions , 2014, ICONIP.

[24]  Alán Aspuru-Guzik,et al.  Convolutional Networks on Graphs for Learning Molecular Fingerprints , 2015, NIPS.

[25]  Mathias Niepert,et al.  Learning Convolutional Neural Networks for Graphs , 2016, ICML.

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

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

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

[29]  Davide Bacciu,et al.  Generative Kernels for Tree-Structured Data , 2018, IEEE Transactions on Neural Networks and Learning Systems.