Gaussian Processes for Machine Learning

C. E. Rasmussen & C. K. I. Williams, Gaussian Processes for Machine Learning , the MIT Press, 2006,ISBN 2006 Massachusetts Institute of 2 RegressionSupervised Learning can be divided into regression and classification the outputs for classification are discrete class labels, regression isconcerned with the prediction of continuous quantities. For example, in a fi-nancial application, one may attempt to predict the price of a commodity asa function of interest rates, currency exchange rates, availability and this chapter we describe Gaussian process methods for regression problems;classification problems are discussed in chapter are several ways to interpret Gaussian process (GP) regression can think of a Gaussian process as defining a distribution over functions,and inference taking place directly in the space of functions, thefunction-spacetwo equivalent viewsview. Although this view is appealing it may initially be difficult to grasp,so we start our exposition in section with the equivalentweight-space viewwhich may be more familiar and accessible to many, and continue in with the function-space view.

2.1.1 The Standard Linear Model We will review the Bayesian analysis of the standard linear regression model with Gaussian noise f(x) = x>w, y = f(x)+ε, (2.1) where x is the input vector, w is a vector of weights (parameters) of the linear bias, offset model, fis the function value and yis …

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