Abstract
We propose deep convolutional Gaussian processes, a deep Gaussian process architecture with convolutional structure. The model is a principled Bayesian framework for detecting hierarchical combinations of local features for image classification. We demonstrate greatly improved image classification performance compared to current convolutional Gaussian process approaches on the MNIST and CIFAR-10 datasets. In particular, we improve state-of-the-art CIFAR-10 accuracy by over 10% points.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
Notes
- 1.
We note that after placing our current manuscript in arXiv in October 2018, a subsequent arXiv manuscript has already extended the proposed deep convolution model by introducing location-dependent kernel [6].
- 2.
References
Abadi, M., et al.: Tensorflow: a system for large-scale machine learning. In: OSDI, vol. 16, pp. 265–283 (2016)
Blei, D.M., Kucukelbir, A., McAuliffe, J.D.: Variational inference: a review for statisticians. J. Am. Stat. Assoc. 112(518), 859–877 (2017)
Blundell, C., Cornebise, J., Kavukcuoglu, K., Wierstra, D.: Weight uncertainty in neural networks. In: International Conference on Machine Learning, pp. 1613–1622 (2015)
Chen, T., Fox, E., Guestrin, C.: Stochastic gradient Hamiltonian Monte Carlo. In: International Conference on Machine Learning, pp. 1683–1691 (2014)
Damianou, A., Lawrence, N.: Deep Gaussian processes. In: AISTATS. PMLR, vol. 31, pp. 207–215 (2013)
Dutordoir, V., van der Wilk, M., Artemev, A., Tomczak, M., Hensman, J.: Translation insensitivity for deep convolutional Gaussian processes. arXiv:1902.05888 (2019)
Duvenaud, D., Rippel, O., Adams, R., Ghahramani, Z.: Avoiding pathologies in very deep networks. In: AISTATS. PMLR, vol. 33, pp. 202–210 (2014)
Duvenaud, D.K., Nickisch, H., Rasmussen, C.E.: Additive Gaussian processes. In: Advances in Neural Information Processing Systems, pp. 226–234 (2011)
Evans, T.W., Nair, P.B.: Scalable Gaussian processes with grid-structured eigenfunctions (GP-GRIEF). In: International Conference on Machine Learning (2018)
Garriga-Alonso, A., Aitchison, L., Rasmussen, C.E.: Deep convolutional networks as shallow Gaussian processes. In: ICLR (2019)
Goodfellow, I., Bengio, Y., Courville, A., Bengio, Y.: Deep Learning, vol. 1. MIT Press, Cambridge (2016)
Havasi, M., Lobato, J.M.H., Fuentes, J.J.M.: Inference in deep Gaussian processes using stochastic gradient Hamiltonian Monte Carlo. In: NIPS (2018)
Hensman, J., Matthews, A., Ghahramani, Z.: Scalable variational Gaussian process classification. In: AISTATS. PMLR, vol. 38, pp. 351–360 (2015)
Huang, G., Liu, Z., Van Der Maaten, L., Weinberger, K.Q.: Densely connected convolutional networks. In: CVPR, vol. 1, p. 3 (2017)
Kingma, D.P., Ba, J.L.: Adam: a method for stochastic optimization. In: ICLR (2014)
Krauth, K., Bonilla, E.V., Cutajar, K., Filippone, M.: AutoGP: exploring the capabilities and limitations of Gaussian process models. In: Uncertainty in Artificial Intelligence (2017)
Krizhevsky, A., Hinton, G.: Learning multiple layers of features from tiny images. Technical report, Citeseer (2009)
Kumar, V., Singh, V., Srijith, P., Damianou, A.: Deep Gaussian processes with convolutional kernels. arXiv preprint arXiv:1806.01655 (2018)
Lee, J., Bahri, Y., Novak, R., Schoenholz, S.S., Pennington, J., Sohl-Dickstein, J.: Deep neural networks as Gaussian processes. In: ICLR (2018)
MacKay, D.J.: A practical Bayesian framework for backpropagation networks. Neural Comput. 4, 448–472 (1992)
Mallat, S.: Understanding deep convolutional networks. Phil. Trans. R. Soc. A 374(2065), 20150203 (2016)
Matthews, A.G.d.G., et al.: GPflow: a Gaussian process library using TensorFlow. J. Mach. Learn. Res. 18, 1–6 (2017)
McInnes, L., Healy, J.: UMAP: uniform manifold approximation and projection for dimension reduction. ArXiv e-prints, February 2018
Rasmussen, C.E.: Gaussian processes in machine learning. In: Bousquet, O., von Luxburg, U., Rätsch, G. (eds.) ML -2003. LNCS (LNAI), vol. 3176, pp. 63–71. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-540-28650-9_4
Rasmussen, C.E., Williams, C.K.: Gaussian Process for Machine Learning. MIT Press, Cambridge (2006)
Remes, S., Heinonen, M., Kaski, S.: Non-stationary spectral kernels. In: Advances in Neural Information Processing Systems, pp. 4642–4651 (2017)
Salimbeni, H., Deisenroth, M.: Doubly stochastic variational inference for deep Gaussian processes. In: Advances in Neural Information Processing Systems, pp. 4588–4599 (2017)
Snelson, E., Ghahramani, Z.: Sparse Gaussian processes using pseudo-inputs. In: Advances in Neural Information Processing Systems, pp. 1257–1264 (2006)
Springerberg, J., Klein, A., Falkner, S., Hutter, F.: Bayesian optimization with robust Bayesian neural networks. In: Advances in Neural Information Processing Systems, pp. 4134–4142 (2016)
Sun, S., Zhang, G., Wang, C., Zeng, W., Li, J., Grosse, R.: Differentiable compositional kernel learning for Gaussian processes. In: ICML. PMLR, vol. 80 (2018)
Tran, G.L., Bonilla, E.V., Cunningham, J.P., Michiardi, P., Filippone, M.: Calibrating deep convolutional Gaussian processes. In: AISTATS. PMLR, vol. 89, pp. 1554–1563 (2019)
Wei, G., Tanner, M.: A Monte Carlo implementation of the EM algorithm and the poor mans data augmentation algorithms. J. Am. Stat. Assoc. 85, 699–704 (1990)
Van der Wilk, M., Rasmussen, C.E., Hensman, J.: Convolutional Gaussian processes. In: Advances in Neural Information Processing Systems, pp. 2849–2858 (2017)
Williams, C.K.: Computing with infinite networks. In: Advances in Neural Information Processing Systems, pp. 295–301 (1997)
Wilson, A., Gilboa, E., Nehorai, A., Cunningham, J.: Fast multidimensional pattern extrapolation with Gaussian processes. In: AISTATS. PMLR, vol. 31 (2013)
Wilson, A., Nickisch, H.: Kernel interpolation for scalable structured Gaussian processes (KISS-GP). In: International Conference on Machine Learning. PMLR, vol. 37, pp. 1775–1784 (2015)
Wilson, A.G., Hu, Z., Salakhutdinov, R.R., Xing, E.P.: Stochastic variational deep kernel learning. In: Advances in Neural Information Processing Systems, pp. 2586–2594 (2016)
Wilson, A.G., Hu, Z., Salakhutdinov, R., Xing, E.P.: Deep kernel learning. In: AISTATS. PMLR, vol. 51, pp. 370–378 (2016)
Acknowledgements
We thank Michael Riis Andersen for his invaluable comments and helpful suggestions.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2020 Springer Nature Switzerland AG
About this paper
Cite this paper
Blomqvist, K., Kaski, S., Heinonen, M. (2020). Deep Convolutional Gaussian Processes. In: Brefeld, U., Fromont, E., Hotho, A., Knobbe, A., Maathuis, M., Robardet, C. (eds) Machine Learning and Knowledge Discovery in Databases. ECML PKDD 2019. Lecture Notes in Computer Science(), vol 11907. Springer, Cham. https://doi.org/10.1007/978-3-030-46147-8_35
Download citation
DOI: https://doi.org/10.1007/978-3-030-46147-8_35
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-46146-1
Online ISBN: 978-3-030-46147-8
eBook Packages: Computer ScienceComputer Science (R0)