Gaussian Processes for Regression
Contact: Stefan Kramer
|Gaussian Processes for Regression|
|Input:||Instances, feature vectors, real-numbered target values|
|Input format:||Dependent on implementation, e.g., Weka's ARFF format|
|Output format:||Dependent on implementation, e.g., Weka's ARFF format|
|User-specified parameters:||Kernel Covariance function, e.g. radial basis function (“squared exponential”)|
|Reporting information:||Performance measures (Correlation coefficient, mean absolute error, root mean squared error, relative absolute error, root relative squared error)|
GPR (Gaussian Processes for Regression) is a way of supervised learning. A Gaussian process is a generalization
of the Gaussian probability distribution. Whereas a probability distribution describes random variables which
are scalars or vectors (for multivariate distributions), a stochastic process governs the properties of functions
Just as a Gaussian distribution is fully specified by its mean and covariance matrix, a Gaussian process
is specified by a mean and a covariance function. Here, the mean is a function of x (which we will often take to
be the zero function), and the covariance is a function C(x, x‟) that expresses the expected covariance between
the values of the function y at the points x and x‟. The function y(x) in any one data modeling problem is
assumed to be a single sample from this Gaussian distribution.
Gaussian processes are already well established models for various spatial and temporal problems – for
example, Brownian motion, Langevin processes and Wiener processes are all examples of Gaussian processes.
Gaussian processes are implementations are available via various software packages and in most programming
languages, e.g. Weka (Java), R, Matlab, python, C, C++.
Bias (instance-selection bias, feature-selection bias, combined instance-selection/feature-selection bias, independence assumptions?, ...)
The chosen covariance function, which encodes the assumption about the function we want to learn, is a bias.
Lazy learning/eager learning
Interpretability of models (black box model?, ...)
Depends on the covariance function (kernel).
Type of Descriptor:
External components: WEKA
Programming language(s): Java
Operating system(s): Linux, Win, Mac OS
Input format: Dependent on implementation, e.g., Weka's ARFF format
Output format: Dependent on implementation, e.g., Weka's ARFF format
[RAS05] Rasmussen, C. E.; Williams, C. K. I. Gaussian Processes for Machine Learning (Adaptive Computation and Machine Learning); The MIT Press: 2005.