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Journal of Machine Learning Research, 11:3011–3015, Gaussian Processes for machine learning (GPML) toolbox. The variational Gaussian approximation revisited.
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Handbook of Markov Chain Monte Carlo, pages 113–162, 2010. On Sparse variational methods and the Kullback-Leiblerĭifferentiation of the Cholesky decomposition.ĪrXiv preprint 1602.07527, February 2016. Scalable Variational Gaussian Process Classification.Īlexander G. MCMC for variationally Sparse Gaussian Processes. James Hensman, Nicolo Fusi, and Neil D Lawrence. GPy: A Gaussian process framework in Python. Gaussian process models with parallelization and GPU acceleration. Zhenwen Dai, Andreas Damianou, James Hensman, and Neil Lawrence. TensorFlow: Large-scale machine learning on heterogeneous systems, Vinyals, Pete Warden, Martin Wattenberg, Martin Wicke, Yuan Yu, and Xiaoqiang Paul Tucker, Vincent Vanhoucke, Vijay Vasudevan, Fernanda Viégas, Oriol Mike Schuster, Jonathon Shlens, Benoit Steiner, Ilya Sutskever, Kunal Talwar,
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Levenberg, Dan Mané, Rajat Monga, Sherry Moore, Derek Murray, Chris Olah, Yangqing Jia, Rafal Jozefowicz, Lukasz Kaiser, Manjunath Kudlur, Josh Sanjay Ghemawat, Ian Goodfellow, Andrew Harp, Geoffrey Irving, Michael Isard, Corrado, Andy Davis, Jeffrey Dean, Matthieu Devin, Martín Abadi, Ashish Agarwal, Paul Barham, Eugene Brevdo, Zhifeng Chen,Ĭraig Citro, Greg S. Error bars shown represent one standard deviation computed from five repeats of the experiment. Figure 1:Ī comparison of iterations of stochastic variational inference per second on the MNIST dataset for GPflow and GPy. James Hensman was supported by an MRC fellowship. Matthews was supported by EPSRC grants EP/I036575/1 and EP/N014162/1. Harris, Rasmus Munk Larsen and Eugene Brevdo. We acknowledge contributions from Valentine Svensson, Dan Marthaler, David J. Relevant references are VGP (Opper and Archambeau, 2009), SGPR (Titsias, 2009), SVGP (Hensman et al., 2013, 2015b) and SGPMC (Hensman et al., 2015a). Table 2: A table showing the inference classes in GPf low. Our main MCMC method is Hamiltonian Monte Carlo (HMC) (Neal, 2010). Note that all the MCMC based inference methods support a Bayesian prior on the hyperparameters, whereas all other methods assume a point estimate. The inference options, which are implemented as classes in GPf low, are summarized in Table 2 Whether or not a given inference method uses variational sparsity is another useful way to categorize it. To this end we support ‘variationally sparse’ methods which ensure that the approximation is scalable and close in a Kullback-Leibler sense to the posterior (Matthews et al., 2016). Another major source of intractability is the adverse scaling of GP methods with the number of data points.
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One source of intractability is non-Gaussian likelihoods, so it is helpful to categorize the available likelihood functionality on this basis. GPf low supports exact inference where possible, as well as a variety of approximation methods. 4 Contributing GP requirements to TensorFlow In the GPU column GPLVM denotes Gaussian process latent variable model and SVI is Stochastic variational inference. Table 1: A summary of the features possessed by existing Gaussian process libraries at the time of writing. Of the available libraries we use TensorFlow (Abadi et al., 2015), as discussed in the next section. Neural network software has made working with neural networks easier by using automatic differentiation to reduce the coding overhead for a user. A central insight here is that many of the features we highlight are well supported in neural network libraries. Having established a desirable set of key design features, the question arises as how best to engineer a Gaussian process library to achieve them.