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

Tonatiuh Peña-CentenoNeil 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.

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

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