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 3 ClassificationIn chapter 2 we have consideredregressionproblems, where the targets arereal valued. Another important class of problems isclassification1problems,where we wish to assign an input patternxto one ofCclasses,C1,.., examples of classification problems are handwritten digit recognition(where we wish to classify a digitized image of a handwritten digit into one often classes 0-9), and the classification of objects detected in astronomical skysurveys into stars or galaxies. (Information on the distribution of galaxies inthe universe is important for theories of the early universe.) These examplesnicely illustrate that classification problems can either be binary (or two-class,binary, multi-classC= 2) or multi-class (C >2).We will focus attention onprobabilistic classification, where test predictionsprobabilisticclassificationta ke the form of class probabilities; this contrasts with methods which provideonly aguessat the class label, and this distinction is analogous to the differencebetween predictive distributions and point predictions in the regression generalization to test cases inherently involves some level of uncertainty,it seems natural to attempt to make predictions in a way that reflects theseuncertaint

C. E. Rasmussen & C. K. I. Williams, Gaussian Processes for Machine Learning, the MIT Press, 2006, ISBN 026218253X. 2006 Massachusetts Institute of Technology.c www.GaussianProcess.org/gpml

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