Gaussian Processes for Regression | Classification

Some pointer advice about the Gaussian process regression 

 

Definition of a Gaussian Process from [1]

Gaussian processes are a simple and general class of models of functions. To be precise, a GP is any distribution over functions such that any finite set of function values f(x1), f(x2), . . . f(xN) have a joint Gaussian distribution (Rasmussen and Williams, 2006, chapter 2).  

 

About the construction of the covariance matrix  [2] 

The covariance matrix is created by pairwise evaluation of the kernel function resulting in an N-dimensional distribution.[2]

Regression is used to find a function (line)that represents a set of data points as closely as possible [2]

 

Definition of a Gaussian Process from [3]

Gaussian processes (GPs) extend multivariate Gaussian distributions to infinite dimensionality. Formally, a Gaussian process generates data located throughout some domain such that any finite subset of the range follows a multivariate Gaussian distribution. 

Covariance functions can be grown in this way ad infinitum, to suit the complexity of your particular data.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 [1] Duvenaud D. Automatic model construction with Gaussian processes[D]. University of Cambridge, 2014.

 [2]  https://www.jgoertler.com/visual-exploration-gaussian-processes/

 [3] Ebden M. Gaussian processes for regression: A quick introduction[J]. The Website of Robotics Research Group in                      Department on Engineering Science, University of Oxford, 2008, 91: 424-436.