Graph Convolutional Gaussian Processes

We propose a novel Bayesian nonparametric method to learn translation-invariant relationships on non-Euclidean domains. The resulting graph convolutional Gaussian processes can be applied to problems in machine learning for which the input observations are functions with domains on general graphs. The structure of these models allows for high dimensional inputs while retaining expressibility, as is the case with convolutional neural networks. We present applications of graph convolutional Gaussian processes to images and triangular meshes, demonstrating their versatility and effectiveness, comparing favorably to existing methods, despite being relatively simple models.

[1]  Alexis Boukouvalas,et al.  GPflow: A Gaussian Process Library using TensorFlow , 2016, J. Mach. Learn. Res..

[2]  Yixin Chen,et al.  An End-to-End Deep Learning Architecture for Graph Classification , 2018, AAAI.

[3]  Ron Kimmel,et al.  Computing geodesic paths on , 1998 .

[4]  Pierre Vandergheynst,et al.  Geometric Deep Learning: Going beyond Euclidean data , 2016, IEEE Signal Process. Mag..

[5]  S. V. N. Vishwanathan,et al.  Graph kernels , 2007 .

[6]  J A Sethian,et al.  A fast marching level set method for monotonically advancing fronts. , 1996, Proceedings of the National Academy of Sciences of the United States of America.

[7]  Roman Garnett,et al.  Propagation kernels: efficient graph kernels from propagated information , 2015, Machine Learning.

[8]  J A Sethian,et al.  Computing geodesic paths on manifolds. , 1998, Proceedings of the National Academy of Sciences of the United States of America.

[9]  James Hensman,et al.  Scalable Variational Gaussian Process Classification , 2014, AISTATS.

[10]  Jonathan Masci,et al.  Geometric Deep Learning on Graphs and Manifolds Using Mixture Model CNNs , 2016, 2017 IEEE Conference on Computer Vision and Pattern Recognition (CVPR).

[11]  Iasonas Kokkinos,et al.  Intrinsic shape context descriptors for deformable shapes , 2012, 2012 IEEE Conference on Computer Vision and Pattern Recognition.

[12]  Carl E. Rasmussen,et al.  Gaussian processes for machine learning , 2005, Adaptive computation and machine learning.

[13]  Paolo Cignoni,et al.  MeshLab: an Open-Source Mesh Processing Tool , 2008, Eurographics Italian Chapter Conference.

[14]  Carl E. Rasmussen,et al.  Manifold Gaussian Processes for regression , 2014, 2016 International Joint Conference on Neural Networks (IJCNN).

[15]  Yin Cheng Ng,et al.  Bayesian Semi-supervised Learning with Graph Gaussian Processes , 2018, NeurIPS.

[16]  Carl E. Rasmussen,et al.  Additive Gaussian Processes , 2011, NIPS.

[17]  Aníbal R. Figueiras-Vidal,et al.  Inter-domain Gaussian Processes for Sparse Inference using Inducing Features , 2009, NIPS.

[18]  Michael J. Black,et al.  FAUST: Dataset and Evaluation for 3D Mesh Registration , 2014, 2014 IEEE Conference on Computer Vision and Pattern Recognition.

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

[20]  Cordelia Schmid,et al.  Convolutional Kernel Networks , 2014, NIPS.

[21]  Neil D. Lawrence,et al.  Deep Gaussian Processes , 2012, AISTATS.

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

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

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

[25]  Peter Händel,et al.  Gaussian Processes Over Graphs , 2018, ICASSP 2020 - 2020 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP).

[26]  Pierre Vandergheynst,et al.  Geodesic Convolutional Neural Networks on Riemannian Manifolds , 2015, 2015 IEEE International Conference on Computer Vision Workshop (ICCVW).

[27]  Carl E. Rasmussen,et al.  Convolutional Gaussian Processes , 2017, NIPS.