A Sparse B ayesian Compression Scheme — The Informative Vector Machine
Kernel based learning algorithms allow the mapping of dataset into an infinite dimensional feature space in which a classification may be perform ed. As such kernel methods represent a powerful approach to the solution of many non-li near problems. However kernel methods do suffer from one unfortunate drawback, the Gra m matrix containsm rows and columns wherem is the number of data-points. Many operations are precluded (e.g. matrix inverseO(m3)) when data-sets containing more than about 104 points are encountered. One approach to resolving these issues is to look for s parse representations of the data-set [7, 5, 2]. A sparse representation contains a reduc ed number of examples. Loosely speaking we are interested in extracting the maximu m amount of information from the minimum number of data-points. To achieve this in a p rincipled 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 methodo logy t determine how much information is gained from each data-point.