Optimising Kernel Parameters and Regularisation Coefficients for Non-linear Discriminant Analysis

Tonatiuh <span>Peña-Centeno</span>; Neil D. Lawrence

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Optimising Kernel Parameters and Regularisation Coefficients for Non-linear Discriminant Analysis

Tonatiuh Peña-Centeno, Neil D. Lawrence

, 2004.

Abstract

In this paper we consider a Bayesian interpretation of Fisher’s discriminant. By relating Rayleigh’s coefficient to a likelihood function and through the choice of a suitable prior we use Bayes’ rule to infer a posterior distribution over projections. Through the use of a Gaussian process prior we show the equivalence of our model to a regularised kernel Fisher’s discriminant. A key advantage of our approach is the facility to determine kernel parameters and the regularisation coefficient through optimisation of the marginalised likelihood of the data.

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Cite this Paper

BibTeX


@Misc{Pena:fbd-tech04,
  title = 	 {Optimising Kernel Parameters and Regularisation Coefficients for Non-linear Discriminant Analysis},
  author = 	 {Peña-Centeno, Tonatiuh and Lawrence, Neil D.},
  year = 	 {2004},
  number =       {CS-04-13},
  pdf = 	 {https://lawrennd.github.io/publications/files/bfdPaper.pdf},
  url = 	 {/publications/pena-fbd-tech04.html},
  abstract = 	 {In this paper we consider a Bayesian interpretation of Fisher's discriminant. By relating Rayleigh's coefficient to a likelihood function and through the choice of a suitable prior we use Bayes' rule to infer a posterior distribution over projections. Through the use of a Gaussian process prior we show the equivalence of our model to a regularised kernel Fisher's discriminant. A key advantage of our approach is the facility to determine kernel parameters and the regularisation coefficient through optimisation of the marginalised likelihood of the data.}
}

Endnote

%0 Generic
%T Optimising Kernel Parameters and Regularisation Coefficients for Non-linear Discriminant Analysis
%A Tonatiuh Peña-Centeno
%A Neil D. Lawrence
%D 2004	
%F Pena:fbd-tech04
%U /publications/pena-fbd-tech04.html
%N CS-04-13
%X In this paper we consider a Bayesian interpretation of Fisher's discriminant. By relating Rayleigh's coefficient to a likelihood function and through the choice of a suitable prior we use Bayes' rule to infer a posterior distribution over projections. Through the use of a Gaussian process prior we show the equivalence of our model to a regularised kernel Fisher's discriminant. A key advantage of our approach is the facility to determine kernel parameters and the regularisation coefficient through optimisation of the marginalised likelihood of the data.

RIS


TY  - GEN
TI  - Optimising Kernel Parameters and Regularisation Coefficients for Non-linear Discriminant Analysis
AU  - Tonatiuh Peña-Centeno
AU  - Neil D. Lawrence
DA  - 2004/01/01	
ID  - Pena:fbd-tech04
IS  - CS-04-13
L1  - https://lawrennd.github.io/publications/files/bfdPaper.pdf
UR  - /publications/pena-fbd-tech04.html
AB  - In this paper we consider a Bayesian interpretation of Fisher's discriminant. By relating Rayleigh's coefficient to a likelihood function and through the choice of a suitable prior we use Bayes' rule to infer a posterior distribution over projections. Through the use of a Gaussian process prior we show the equivalence of our model to a regularised kernel Fisher's discriminant. A key advantage of our approach is the facility to determine kernel parameters and the regularisation coefficient through optimisation of the marginalised likelihood of the data.
ER  -

APA


Peña-Centeno, T. & Lawrence, N.D.. (2004). Optimising Kernel Parameters and Regularisation Coefficients for Non-linear Discriminant Analysis. (CS-04-13) Available from /publications/pena-fbd-tech04.html.