codemarsyu/gpflow

Gaussian processes in tensorflow

GPflow

GPflow is a package for building Gaussian process models in python, using TensorFlow. It was originally created and is now managed by James Hensman and Alexander G. de G. Matthews. The full list of contributors (in alphabetical order) is James Hensman, Alexander G. de G. Matthews and Mark van der Wilk. GPflow is an open source project so if you feel you have some relevant skills and are interested in contributing then please do contact us.

Install

1) Install Tensorflow

To make Gaussian processes work, we've had to add some extra functionality to TensorFlow. Our code is now included in the main TensorFlow repository and we are waiting for it to be part of the next release. Until then we have compiled pip packages from the TensorFlow master branch for you to use. Be aware that changing your installation of TensorFlow may change how it works for you.

EITHER:

1a) Install Tensorflow using Pip. Best option for most users.

The sequence of commands for Linux is:

pip uninstall tensorflow
pip install http://mlg.eng.cam.ac.uk/matthews/GPflow/python_packages/version_0.4/linux/tensorflow-0.8.0rc0-py2-none-any.whl

The sequence of commands for Mac OS is:

pip uninstall tensorflow
pip install http://mlg.eng.cam.ac.uk/matthews/GPflow/python_packages/version_0.4/osx/tensorflow-0.8.0rc0-py2-none-any.whl

OR:

1b) Install Tensorflow fork from sources.

For more information see this page.

2) install package

GPflow is a pure python library for now, so you could just add it to your path (we use python setup.py develop) or try an install python setup.py install (untested). You can run the tests with python setup.py test.

What's the difference between GPy and GPflow?

GPflow has origins in GPy by the GPy contributors, and much of the interface is intentionally similar for continuity (though some parts of the interface may diverge in future). GPflow has a rather different remit from GPy though:

• GPflow attempts to leverage tensorflow for faster/bigger computation
• GPflow has much less code than GPy, mostly because all gradient computation is handled by tensorflow.
• GPflow focusses on variational inference and MCMC -- there is no expectation propagation or Laplace approximation.
• GPflow does not do latent variable models (GPLVMs).
• GPflow does not have any plotting functionality.
• GPflow is not meant as a tool to teach about GPs. GPy is much better at that.

What models are implemented?

GPflow has a slew of kernels that can be combined in a similar way to GPy (see this tutorial). As for inference, the options are currently:

Regression

For GP regression with Gaussian noise, it's possible to marginalize the function values exactly: you'll find this in GPflow.gpr.GPR. You can do maximum liklelihood or MCMC for the covariance function parameters (notebook).

It's also possible to do Sparse GP regression using the GPflow.sgpr.SGPR class. This is based on [4].

MCMC

For non-Gaussian likelohoods, GPflow has a model that can jointly sample over the function values and the covariance parameters: GPflow.gpmc.GPMC. There's also a sparse equivalent in GPflow.sgpmc.SGPMC, based on a recent paper [1]. This notebook introduces the interface.

Variational inference

It's often sufficient to approximate the function values as a Gaussian, for which we follow [2] in GPflow.vgp.VGP. In addition, there is a sparse version based on [3] in GPflow.svgp.SVGP. In the Gaussian likelihood case some of the optimization may be done analytically as discussed in [4] and implemented in GPflow.sgpr.SGPR . All of the sparse methods in GPflow are solidified in [5].

The following table summarizes the model options in GPflow.

	Gaussian likelihood	Non-Gaussian (variational)	Non-Gaussian (MCMC)
Full-covariance	GPflow.gpr.GPR	GPflow.vgp.VGP	GPflow.gpmc.GPMC
Sparse approximation	GPflow.sgpr.SGPR	GPflow.svgp.SVGP	GPflow.sgpmc.SGPMC

References

[1] MCMC for Variationally Sparse Gaussian Processes J Hensman, A G de G Matthews, M Filippone, Z Ghahramani Advances in Neural Information Processing Systems, 1639-1647

[2] The variational Gaussian approximation revisited M Opper, C Archambeau Neural computation 21 (3), 786-792

[3] Scalable Variational Gaussian Process Classification J Hensman, A G de G Matthews, Z Ghahramani Proceedings of AISTATS 18, 2015

[4] Variational Learning of Inducing Variables in Sparse Gaussian Processes. M Titsias Proceedings of AISTATS 12, 2009

[5] On Sparse variational methods and the Kullback-Leibler divergence between stochastic processes A G de G Matthews, J Hensman, R E Turner, Z Ghahramani Proceedings of AISTATS 19, 2016

Acknowledgements

James Hensman was supported by an MRC fellowship and Alexander G. de G. Matthews was supported by EPSRC grant EP/I036575/1.