Extended Linear Models with Gaussian Priors  Joaquin QuiñoneroCandela
 Abstract  In extended linear models the input space is projected onto a feature space by
means of an arbitrary nonlinear transformation. A linear model is then applied to
the feature space to construct the model output. The dimension of the feature
space can be very large, or even infinite, giving the model a very big flexibility.
Support Vector Machines (SVM's) and Gaussian processes are two examples of
such models. In this technical report I present a model in which the dimension of
the feature space remains finite, and where a Bayesian approach is used to train
the model with Gaussian priors on the parameters. The Relevance Vector
Machine, introduced by Tipping, is a particular case of such a model. I give the
detailed derivations of the expectationmaximisation (EM) algorithm used in the
training. These derivations are not found in the literature, and might be helpful for
newcomers.  Keywords  linear models, bayes, Gaussian processes, Relevance Vector Machine, ExpectationMaximization algorithm  Type  Technical report  Year  2002  Publisher  Informatics and Mathematical Modelling, Technical University of Denmark  Address  Richard Petersens Plads, Building 321, DK2800 Kongens Lyngby, Denmark  Electronic version(s)  [ps]  BibTeX data  [bibtex]  IMM Group(s)  Intelligent Signal Processing 
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