Two New Papers by CSML Members

Two papers of CSML members Prof. Mark Girolami and Dr. Arthur Gretton have recently been published. These two are the first papers to carry the official CSML affiliation.

  • Markov Chain Monte Carlo Methods for State-Space Models with Point Process Observations
    Ke Yuan, Mark Girolami, Mahesan Niranjan
    Neural Computation, June 2012, Vol. 24, No. 6, Pages 1462-1486, Link

    This letter considers how a number of modern Markov chain Monte Carlo (MCMC) methods can be applied for parameter estimation and inference in state-space models with point process observations. We quantified the efficiencies of these MCMC methods on synthetic data, and our results suggest that the Reimannian manifold Hamiltonian Monte Carlo method offers the best performance. We further compared such a method with a previously tested variational Bayes method on two experimental data sets. Results indicate similar performance on the large data sets and superior performance on small ones. The work offers an extensive suite of MCMC algorithms evaluated on an important class of models for physiological signal analysis.

  • A Kernel Two-Sample Test
    Arthur Gretton, Karsten M. Borgwardt, Malte J. Rasch, Bernhard Schölkopf, Alexander Smola
    JMLR, March 2012, Vol. 13, Pages 723−773, Link

    We propose a framework for analyzing and comparing distributions, which we use to construct statistical tests to determine if two samples are drawn from different distributions. Our test statistic is the largest difference in expectations over functions in the unit ball of a reproducing kernel Hilbert space (RKHS), and is called the maximum mean discrepancy (MMD). We present two distribution-free tests based on large deviation bounds for the MMD, and a third test based on the asymptotic distribution of this statistic. The MMD can be computed in quadratic time, although efficient linear time approximations are available. Our statistic is an instance of an integral probability metric, and various classical metrics on distributions are obtained when alternative function classes are used in place of an RKHS. We apply our two-sample tests to a variety of problems, including attribute matching for databases using the Hungarian marriage method, where they perform strongly. Excellent performance is also obtained when comparing distributions over graphs, for which these are the first such tests.