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

[edit]

Tonatiuh Peña-Centeno
Neil D. Lawrence, University of Sheffield

Related Material

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.


@TechReport{pena-fbd-tech04,
  title = 	 {Optimising Kernel Parameters and Regularisation Coefficients for Non-linear Discriminant Analysis},
  author = 	 {Tonatiuh Peña-Centeno and Neil D. Lawrence},
  year = 	 {2004},
  institution = 	 {The University of Sheffield, Department of Computer Science},
  number =       {CS-04-13},
  month = 	 {00},
  edit = 	 {https://github.com/lawrennd//publications/edit/gh-pages/_posts/2004-01-01-pena-fbd-tech04.md},
  url =  	 {http://inverseprobability.com/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.},
  key = 	 {Pena:fbd-tech04},
  linkpsgz =  {ftp://ftp.dcs.shef.ac.uk/home/neil/bfdPaper.ps.gz},
  linksoftware = {http://inverseprobability.com/bfd/},
  group = 	 {shefml}
 

}
%T Optimising Kernel Parameters and Regularisation Coefficients for Non-linear Discriminant Analysis
%A Tonatiuh Peña-Centeno and Neil D. Lawrence
%B 
%D 
%F pena-fbd-tech04	
%P --
%R 
%U http://inverseprobability.com/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.
TY  - CPAPER
TI  - Optimising Kernel Parameters and Regularisation Coefficients for Non-linear Discriminant Analysis
AU  - Tonatiuh Peña-Centeno
AU  - Neil D. Lawrence
PY  - 2004/01/01
DA  - 2004/01/01	
ID  - pena-fbd-tech04	
SP  - 
EP  - 
UR  - http://inverseprobability.com/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  -

Peña-Centeno, T. & Lawrence, N.D.. (2004). Optimising Kernel Parameters and Regularisation Coefficients for Non-linear Discriminant Analysis.(CS-04-13):-