Arthur Gretton
Hypothesis testing using pairwise distances and associated kernels.
Thu, 05/03/2012 - 15:01 — SomNambulAuthors: Kenji Fukumizu, Arthur Gretton, Bharath Sriperumbudur, Dino Sejdinovic
Subjects: Learning
AbstractWe provide a unifying framework linking two classes of statistics used in
two-sample and independence testing: on the one hand, the energy distances and
distance covariances from the statistics literature; on the other, distances
between embeddings of distributions to reproducing kernel Hilbert spaces
(RKHS), as established in machine learning. The equivalence holds when energy
distances are computed with semimetrics of negative type, in which case a
kernel may be defined such that the RKHS distance between distributions
corresponds exactly to the energy distance.- Read more
- 3 comments
- login or register to post comments
Discussion of: Brownian distance covariance.
Wed, 10/06/2010 - 15:01 — SomNambulAuthors: Kenji Fukumizu, Bharath K. Sriperumbudur, Arthur Gretton
Subjects: Applications
AbstractDiscussion on "Brownian distance covariance" by G\'{a}bor J. Sz\'{e}kely and
Maria L. Rizzo [arXiv:1010.0297]Kernel Bayes' rule.
Thu, 09/30/2010 - 15:01 — SomNambulAuthors: Kenji Fukumizu, Arthur Gretton, Le Song
Subjects: Machine Learning
AbstractA kernel method is proposed for realizing Bayes' rule, based on
representations of probability distributions in reproducing kernel Hilbert
spaces (RKHS). The empirical RKHS embeddings of the conditional probabilities
and prior are expressed as feature mappings of samples, and an RKHS embedding
of the posterior distribution is computed, again based on a feature mapping of
a sample. This kernel Bayes' rule can be applied to a wide variety of
nonparametric Bayesian inference problems. As an example, the approach is used
in filtering with a nonparametric state-space model.On integral probability metrics, \phi-divergences and binary classification.
Thu, 08/20/2009 - 23:06 — SomNambulAuthors: Kenji Fukumizu, Bharath K. Sriperumbudur, Arthur Gretton, Bernhard Schölkopf, Gert R. G. Lanckriet
Subjects: Information Theory
AbstractA class of distance measures on probabilities -- the integral probability
metrics (IPMs) -- is addressed: these include the Wasserstein distance, Dudley
metric, and Maximum Mean Discrepancy. IPMs have thus far mostly been used in
more abstract settings, for instance as theoretical tools in mass
transportation problems, and in metrizing the weak topology on the set of all
Borel probability measures defined on a metric space.
User login
