One sketch for all: Theory and Application of Conditional Random Sampling

Abstract

Conditional Random Sampling (CRS) was originally proposed for efficiently computing pairwise (l2, l1) distances, in static, large-scale, and sparse data. This study modifies the original CRS and extends CRS to handle dynamic or streaming data, which much better reflect the real-world situation than assuming static data. Compared with many other sketching algorithms for dimension reductions such as stable random projections, CRS exhibits a significant advantage in that it is “one-sketch-for-all. ” In particular, we demonstrate the effectiveness of CRS in efficiently computing the Hamming norm, the Hamming distance, the lp distance, and the χ 2 distance. A generic estimator and an approximate variance formula are also provided, for approximating any type of distances. We recommend CRS as a promising tool for building highly scalable systems, in machine learning, data mining, recommender systems, and information retrieval. 1