TY - JOUR
AU - Peng, Richard
AB -  p Row Sampling by Lewis Weights Richard Peng rpeng@mit.edu M.I.T. M.I.T. Michael B. Cohen micohen@mit.edu ABSTRACT We give a simple algorithm to efficiently sample the rows of a matrix while preserving the p-norms of its product with vectors. Given an n-by-d matrix A, we find with high probability and in input sparsity time an A consisting of about d log d rescaled rows of A such that Ax 1 is close to A x 1 for all vectors x . We also show similar results for all p that give nearly optimal sample bounds in input sparsity time. Our results are based on sampling by "Lewis weights", which can be viewed as statistical leverage scores of a reweighted matrix. We also give an elementary proof of the guarantees of this sampling process for 1 . 1. INTRODUCTION Randomized sampling is an important tool in the design of efficient algorithms. A random subset often preserves key properties of the entire data set, allowing one to run algorithms on a small sample. A particularly useful instance of this phenomenon is row sampling of matrices. For a n × d matrix A where n d and any error parameter > 0, 
TI - L p Row Sampling by Lewis Weights
DA - 2015-06-14
UR - https://www.deepdyve.com/lp/association-for-computing-machinery/l-p-row-sampling-by-lewis-weights-miHUk01Xqh
DP - DeepDyve
ER -