On the Noise Model of Support Vector Machines Regression
Authors: Massimiliano Pontil, Sayan Mukherjee and Federico Girosi.
Source: Lecture Notes in Artificial Intelligence Vol. 1968,
2000, 316 - 324.
Abstract.
Support Vector Machines Regression (SVMR) is a learning technique where the
goodness of fit is measured not by the usual quadratic loss function
(the mean square error), but by a different loss function
called the -Insensitive Loss Function (ILF),
which is similar to loss functions used in the field of robust statistics.
The quadratic loss function is well justified under the assumption of Gaussian additive noise.
However, the noise model underlying the choice of the ILF is not clear. In this
paper the use of the ILF is justified under the assumption that the noise is
additive and Gaussian, where the variance and mean of the
Gaussian are random variables. The probability distributions for the variance
and mean will be stated explicitly. While this work is presented in the
framework of SVMR, it can be extended to justify non-quadratic loss functions
in any Maximum Likelihood or Maximum A Posteriori approach. It applies not
only to the ILF, but to a much broader class of loss functions.
©Copyright 2000 Springer
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