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v0.3.3 paper submission. (#243)
# GPflow GPflow is a package for building Gaussian process models in python, using [TensorFlow](http://www.tensorflow.org). It was originally created and is now managed by [James Hensman](http://www.lancaster.ac.uk/staff/hensmanj/) and [Alexander G. de G. Matthews](http://mlg.eng.cam.ac.uk/?portfolio=alex-matthews). The full list of [contributors](http://github.com/GPflow/GPflow/graphs/contributors) (in alphabetical order) is Alexis Boukouvalas, Keisuke Fujii, James Hensman, Pablo Leon, Alexander G. de G. Matthews, Valentine Svensson 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. [![Python2.7 status](https://codeship.com/projects/26b43920-e96e-0133-3481-02cde9680eda/status?branch=master)](https://codeship.com/projects/147609) [![Python3.5 Status](https://travis-ci.org/GPflow/GPflow.svg?branch=master)](https://travis-ci.org/GPflow/GPflow) [![Coverage Status](http://codecov.io/github/GPflow/GPflow/coverage.svg?branch=master)](http://codecov.io/github/GPflow/GPflow?branch=master) [![Documentation Status](https://readthedocs.org/projects/gpflow/badge/?version=latest)](http://gpflow.readthedocs.io/en/latest/?badge=latest) # Install ## 1) Install TensorFlow. Please see instructions on the main TensorFlow [webpage](https://www.tensorflow.org/versions/r0.10/get_started/os_setup.html#download-and-setup). You will need version 0.11. We find that for most users pip installation is the fastest way to get going. ## 2) install package GPflow includes some tensorflow extensions that are compiled when you run setup.py. For those interested in modifying the source of GPflow, we recommend ``` python setup.py develop ``` but installation should work well too: ``` python setup.py install ``` You can run the tests with `python setup.py test`. # What's the difference between GPy and GPflow? GPflow has origins in [GPy](http://github.com/sheffieldml/gpy) by the [GPy contributors](https://github.com/SheffieldML/GPy/graphs/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](http://gpss.cc). # What models are implemented? GPflow has a slew of kernels that can be combined in a similar way to GPy ([see this tutorial](https://github.com/SheffieldML/notebook/blob/master/GPy/basic_kernels.ipynb)). 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 likelihood or MCMC for the covariance function parameters ([notebook](https://github.com/GPflow/GPflow/blob/master/doc/source/notebooks/regression.ipynb)). It's also possible to do Sparse GP regression using the `GPflow.sgpr.SGPR` class. This is based on . #### MCMC For non-Gaussian likelihoods, 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 . This [notebook](https://github.com/GPflow/GPflow/blob/master/doc/source/notebooks/Sparse%20mcmc%20demo.ipynb) introduces the interface. #### Variational inference It's often sufficient to approximate the function values as a Gaussian, for which we follow  in `GPflow.vgp.VGP`. In addition, there is a sparse version based on  in `GPflow.svgp.SVGP`. In the Gaussian likelihood case some of the optimization may be done analytically as discussed in  and implemented in `GPflow.sgpr.SGPR` . All of the sparse methods in GPflow are solidified in . The following table summarizes the model options in GPflow. | | Gaussian <br> likelihood | Non-Gaussian <br> (variational) | Non-Gaussian <br> (MCMC)| | --- | --- | --- | --- | | Full-covariance | `GPflow.gpr.GPR` | `GPflow.vgp.VGP` | `GPflow.gpmc.GPMC`| | Sparse approximation | `GPflow.sgpr.SGPR` | `GPflow.svgp.SVGP` | `GPflow.sgpmc.SGPMC` | ### References  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  The variational Gaussian approximation revisited M Opper, C Archambeau Neural computation 21 (3), 786-792  Scalable Variational Gaussian Process Classification J Hensman, A G de G Matthews, Z Ghahramani Proceedings of AISTATS 18, 2015  Variational Learning of Inducing Variables in Sparse Gaussian Processes. M Titsias Proceedings of AISTATS 12, 2009  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.