Kernel based learning algorithms allow the mapping of data-set into an infinite dimensional feature space in which a classification may be performed. As such kernel methods represent a powerful approach to the solution of many non-linear problems. However kernel methods do suffer from one unfortunate drawback, the Gram matrix contains m rows and columns where m is the number of data-points. Many operations are therefore precluded (e.g. matrix inverse $O(m^3)$) when data-sets containing more than about $10^4$ points are encountered. One approach to resolving these issues is to look for sparse representations of the data-set A sparse representation contains a reduced number of examples. Loosely speaking we are interested in extracting the maximum amount of information from the minimum number of data-points. To achieve this in a principled manner we are interested in estimating the amount of information each data-point contains. In the framework presented here we make use of the Bayesian methodology to determine how much information is gained from each data-point.

%T A Sparse Bayesian Compression Scheme — The Informative Vector Machine
%A Neil D. Lawrence and Ralf Herbrich
%B
%D
%F lawrence-informative01
%P --
%R
%U http://inverseprobability.com/publications/lawrence-informative01.html
%X Kernel based learning algorithms allow the mapping of data-set into an infinite dimensional feature space in which a classification may be performed. As such kernel methods represent a powerful approach to the solution of many non-linear problems. However kernel methods do suffer from one unfortunate drawback, the Gram matrix contains m rows and columns where m is the number of data-points. Many operations are therefore precluded (e.g. matrix inverse $O(m^3)$) when data-sets containing more than about $10^4$ points are encountered. One approach to resolving these issues is to look for sparse representations of the data-set A sparse representation contains a reduced number of examples. Loosely speaking we are interested in extracting the maximum amount of information from the minimum number of data-points. To achieve this in a principled manner we are interested in estimating the amount of information each data-point contains. In the framework presented here we make use of the Bayesian methodology to determine how much information is gained from each data-point.

TY - CPAPER
TI - A Sparse Bayesian Compression Scheme — The Informative Vector Machine
AU - Neil D. Lawrence
AU - Ralf Herbrich
PY - 2001/01/01
DA - 2001/01/01
ID - lawrence-informative01
SP -
EP -
UR - http://inverseprobability.com/publications/lawrence-informative01.html
AB - Kernel based learning algorithms allow the mapping of data-set into an infinite dimensional feature space in which a classification may be performed. As such kernel methods represent a powerful approach to the solution of many non-linear problems. However kernel methods do suffer from one unfortunate drawback, the Gram matrix contains m rows and columns where m is the number of data-points. Many operations are therefore precluded (e.g. matrix inverse $O(m^3)$) when data-sets containing more than about $10^4$ points are encountered. One approach to resolving these issues is to look for sparse representations of the data-set A sparse representation contains a reduced number of examples. Loosely speaking we are interested in extracting the maximum amount of information from the minimum number of data-points. To achieve this in a principled manner we are interested in estimating the amount of information each data-point contains. In the framework presented here we make use of the Bayesian methodology to determine how much information is gained from each data-point.
ER -

Lawrence, N.D. & Herbrich, R.. (2001). A Sparse Bayesian Compression Scheme — The Informative Vector Machine.:-

%T A Sparse Bayesian Compression Scheme — The Informative Vector Machine
%A Neil D. Lawrence and Ralf Herbrich
%B
%D
%F /lawrence-informative01
%P --
%R
%U http://inverseprobability.com/publications/lawrence-informative01.html
%X Kernel based learning algorithms allow the mapping of data-set into an infinite dimensional feature space in which a classification may be performed. As such kernel methods represent a powerful approach to the solution of many non-linear problems. However kernel methods do suffer from one unfortunate drawback, the Gram matrix contains m rows and columns where m is the number of data-points. Many operations are therefore precluded (e.g. matrix inverse $O(m^3)$) when data-sets containing more than about $10^4$ points are encountered. One approach to resolving these issues is to look for sparse representations of the data-set A sparse representation contains a reduced number of examples. Loosely speaking we are interested in extracting the maximum amount of information from the minimum number of data-points. To achieve this in a principled manner we are interested in estimating the amount of information each data-point contains. In the framework presented here we make use of the Bayesian methodology to determine how much information is gained from each data-point.

TY - CPAPER
TI - A Sparse Bayesian Compression Scheme — The Informative Vector Machine
AU - Neil D. Lawrence
AU - Ralf Herbrich
PY - 2001/01/01
DA - 2001/01/01
ID - /lawrence-informative01
SP -
EP -
UR - http://inverseprobability.com/publications/lawrence-informative01.html
AB - Kernel based learning algorithms allow the mapping of data-set into an infinite dimensional feature space in which a classification may be performed. As such kernel methods represent a powerful approach to the solution of many non-linear problems. However kernel methods do suffer from one unfortunate drawback, the Gram matrix contains m rows and columns where m is the number of data-points. Many operations are therefore precluded (e.g. matrix inverse $O(m^3)$) when data-sets containing more than about $10^4$ points are encountered. One approach to resolving these issues is to look for sparse representations of the data-set A sparse representation contains a reduced number of examples. Loosely speaking we are interested in extracting the maximum amount of information from the minimum number of data-points. To achieve this in a principled manner we are interested in estimating the amount of information each data-point contains. In the framework presented here we make use of the Bayesian methodology to determine how much information is gained from each data-point.
ER -

Lawrence, N.D. & Herbrich, R.. (2001). A Sparse Bayesian Compression Scheme — The Informative Vector Machine.:-