The invention is an improved retrieval system and method. Many pattern recognition tasks, including estimation, classification, and the finding of similar objects, make use of linear models. For example, many text retrieval systems represent queries as linear functions, and retrieve documents whose vector representation has a high dot product with the query. The fundamental operation in such tasks is the computation of the dot product between a query vector and a large database of instance vectors. Often instance vectors which have high dot products with the query are of interest. The invention relates to a random sampling based retrieval system that can identify, for any given query vector, those instance vectors which have large dot products, while avoiding explicit computation of all dot products.