# A Sparse Bayesian Compression Scheme — The Informative Vector Machine

Neil D. Lawrence, University of Sheffield
Ralf Herbrich, Amazon

#### Abstract

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.:-