TY - RPRT

T1 - Extended Linear Models with Gaussian Priors

AU - Quinonero, Joaquin

PY - 2002

Y1 - 2002

N2 - In extended linear models the input space is projected onto a feature space by
means of an arbitrary non-linear 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 expectation-maximisation (EM) algorithm used in the
training. These derivations are not found in the literature, and might be helpful for
newcomers.

AB - In extended linear models the input space is projected onto a feature space by
means of an arbitrary non-linear 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 expectation-maximisation (EM) algorithm used in the
training. These derivations are not found in the literature, and might be helpful for
newcomers.

KW - Relevance Vector Machine

KW - bayes

KW - Gaussian processes

KW - linear models

KW - Expectation-Maximization algorithm

M3 - Report

BT - Extended Linear Models with Gaussian Priors

ER -