Welcome to the lab for the Gaussian process section at the Machine Learning Summer School in Sydney.

This notebook provides you with the guide to your lab classes for Gaussian processes. The lab classes are intended to help get you familiar with modeling with Gaussian processes as

The lab classes are based on our two software packages, `pods`

which is used for access to datasets and `GPy`

(release 21st November 2014) for Gaussian processes. You can install the GPy framework with

```
pip install GPy
```

As well as the GPy software we use our `pods`

software for 'open data science' for access to data sets and other resources.

```
pip install -pre pods
```

on some systems you may need to use `pip install -pre pods`

to allow the prerelease to install.

As well as these lab classes here are a range of tutorials on how to use `GPy`

, many of which are written by members of the Sheffield research group. `GPy`

is under active development and is released under a BSD license, you'd also be very welcome to contribute!

Before you start, if you aren't familiar with probabilistic processes, the following lab classes from the GPRS schools might be useful. The first session will allow you to become familiar with the Jupyter (the ipython notebook) and start to work with Gaussian processes.

- [Welcome to
`Jupyter`

](./gprs/jupyter introduction.ipynb) A quick introduction to`Jupyter`

,`python`

and`numpy`

. - [Introduction to Probabilistic Regression](./gprs/probabilistic interpretations of regression.ipynb) A review of least squares, basis function modelling and the probabilistic interpretation of least squares.
- [Introduction to Bayesian Regression](./gprs/bayesian approach to regression.ipynb) Introducing priors over parameters and averaging over solutions.

The session will focus on Gaussian process models and developing covariance functions.

- [Introduction to Gaussian Processes](./gaussian process introduction.ipynb) We move from the Bayesian regression with polynomials to Gaussian process perspectives by looking at the priors over the function directly.
- [GPy: Introduction through Covariance Functions](./GPy introduction covariance functions.ipynb)
`GPy`

is a Python Gaussian process framework that implements many of the ideas we'll see in the course. In this session we introduce its covariance functions and sample from the associated Gaussian processes. - [Gaussian Process Regression with GPy](./GPy gaussian process regression.ipynb) In this example we show how to do a simple regression model using Gaussian processes in GPy.
- [Optimizing Gaussian Processes](./GPy optimizing gaussian processes.ipynb) The parameters of the covariance function can be optimized. In this example we show how to optimize the parameters of the covariance function. (TODO HMC)

Things we haven't had time to cover in the MLSS can be found below.

Gaussian processes for learning vector valued functions.

- [Multiple Output GPs](./gprs/multiple outputs.ipynb)
- [TODO Differential Equations and Gaussian Processes](./gprs/GP differential equation.ipynb)

These examples look at approximations for speeding up inference in Gaussian processes and/or making inference tractable.

- [Low Rank Approximations for Gaussian Processes](./gprs/low rank approximations.ipynb)
- [Non Gaussian Likelihoods](./gprs/non gaussian likelihoods.ipynb)
- [Low Rank and Non Gaussian](./gprs/low rank and non gaussian.ipynb)

These examples look at dimensionality reduction with Gaussian processes.

- [Dimensionality Reduction with Gaussian Processes](./gprs/dimensionality reduction with gaussian processes.ipynb)

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