A Hilbert Space Embedding for Distributions (invited lecture for ALT 2007) Authors: Alexander J. Smola, Arthur Gretton, Karsten Borgwardt, Le Song, and Bernhard Schölkopf Affiliation: Machine Learning Program Leader, National ICT Australia / ANU, Canberra, Australia. Abstract. We describe a technique for comparing distributions without the need for density estimation as an intermediate step. Our approach relies on mapping the distributions into a reproducing kernel Hilbert space. Applications of this technique can be found in two-sample tests, which are used for determining whether two sets of observations arise from the same distribution, covariate shift correction, local learning, measures of independence, and density estimation. ©Copyright 2007 Authors