M. P. Wand

University of Technology Sydney, Sydney, New South Wales, Australia

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Publications (117)194.24 Total impact

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    ABSTRACT: A new data science tool named wavelet-based gradient boosting is proposed and tested. The approach is special case of componentwise linear least squares gradient boosting, and involves wavelet functions of the original predictors. Wavelet-based gradient boosting takes advantages of the approximate \(\ell _1\) penalization induced by gradient boosting to give appropriate penalized additive fits. The method is readily implemented in R and produces parsimonious and interpretable regression fits and classifiers.
    No preview · Article · Jan 2014 · Statistics and Computing
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    ABSTRACT: We investigate mean field variational approximate Bayesian inference for models that use continuous distributions, Horseshoe, Negative-Exponential-Gamma and Generalized Double Pareto, for sparse signal shrinkage. Our principal finding is that the most natural, and simplest, mean field variational Bayes algorithm can perform quite poorly due to posterior dependence among auxiliary variables. More sophisticated algorithms, based on special functions, are shown to be superior. Continued fraction approximations via Lentz’s Algorithm are developed to make the algorithms practical.
    No preview · Article · Jan 2014 · Electronic Journal of Statistics
  • Tung H. Pham · John T. Ormerod · M. P. Wand
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    ABSTRACT: A fast mean field variational Bayes (MFVB) approach to nonparametric regression when the predictors are subject to classical measurement error is investigated. It is shown that the use of such technology to the measurement error setting achieves reasonable accuracy. In tandem with the methodological development, a customized Markov chain Monte Carlo method is developed to facilitate the evaluation of accuracy of the MFVB method.
    No preview · Article · Dec 2013 · Computational Statistics & Data Analysis
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    Alan Huang · M. P. Wand
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    ABSTRACT: A family of prior distributions for covariance matrices is studied. Members of the family possess the attractive property of all standard deviation and correlation parameters being marginally noninformative for particular hyperparameter choices. Moreover, the family is quite simple and, for approximate Bayesian inference techniques such as Markov chain Monte Carlo and mean field variational Bayes, has tractability on par with the Inverse-Wishart conjugate family of prior distributions. A simulation study shows that the new prior distributions can lead to more accurate sparse covariance matrix estimation.
    Preview · Article · Jun 2013
  • M.P. Wand

    No preview · Article · Dec 2012 · Australian & New Zealand Journal of Statistics
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    Peter Hall · Tung Pham · M. P. Wand · S. S. J. Wang
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    ABSTRACT: We derive the precise asymptotic distributional behavior of Gaussian variational approximate estimators of the parameters in a single-predictor Poisson mixed model. These results are the deepest yet obtained concerning the statistical properties of a variational approximation method. Moreover, they give rise to asymptotically valid statistical inference. A simulation study demonstrates that Gaussian variational approximate confidence intervals possess good to excellent coverage properties, and have a similar precision to their exact likelihood counterparts.
    Preview · Article · Feb 2012 · The Annals of Statistics
  • John T. Ormerod · M. P. Wand

    No preview · Article · Jan 2012 · Technometrics
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    Sarah E. Nevillea · M. P. Wand
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    ABSTRACT: We devise a variational Bayes algorithm for fast approximate inference in Bayesian Generalized Extreme Value additive model analysis. Such models are useful for flexibly assessing the impact of continuous predictor variables on sample extremes. The new methodology allows large Bayesian models to be fitted and assessed without the significant computing costs of Monte Carlo methods.© 2010 Published by Elsevier Ltd. Selection and/or peer-review under responsibility of Alfred Stein.
    Preview · Article · Dec 2011
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    ABSTRACT: We develop strategies for mean field variational Bayes approximate inference for Bayesian hierarchical models containing elaborate distributions. We loosely define elaborate distributions to be those having more complicated forms compared with common distributions such as those in the Normal and Gamma families. Examples are Asymmetric Laplace, Skew Normal and Generalized Extreme Value distributions. Such models suffer from the difficulty that the parameter updates do not admit closed form solutions. We circumvent this problem through a combination of (a) specially tailored auxiliary variables, (b) univariate quadrature schemes and (c) finite mixture approximations of troublesome density functions. An accuracy assessment is conducted and the new methodology is illustrated in an application.
    Full-text · Article · Dec 2011
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    Christel FAES · J. T. Ormerod · M. P. Wand
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    ABSTRACT: Bayesian hierarchical models are attractive structures for conducting regression analyses when the data are subject to missingness. However, the requisite probability calculus is challenging and Monte Carlo methods typically are employed. We develop an alternative approach based on deterministic variational Bayes approximations. Both parametric and nonparametric regression are considered. Attention is restricted to the more challenging case of missing predictor data. We demonstrate that variational Bayes can achieve good accuracy, but with considerably less computational overhead. The main ramification is fast approximate Bayesian inference in parametric and nonparametric regression models with missing data. Supplemental materials accompany the online version of this article.
    Full-text · Article · Sep 2011 · Journal of the American Statistical Association
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    Sarah E. Neville · M. J. Palmer · M. P. Wand
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    ABSTRACT: We develop Mean Field Variational Bayes methodology for fast approximate inference in Bayesian Generalized Extreme Value additive model analysis. Such models are useful for flexibly assessing the impact of continuous predictor variables on sample extremes. The new methodology allows large Bayesian models to be fitted and assessed without the significant computing costs of Markov Chain Monte Carlo methods. We illustrate our new methodology with maximum rainfall data from the Sydney, Australia, hinterland. Comparisons are made between the Mean Field Variational Bayes and Markov Chain Monte Carlo approaches.
    Preview · Article · Aug 2011 · Australian & New Zealand Journal of Statistics
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    S. S. J. Wang · M. P. Wand
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    ABSTRACT: We demonstrate and critique the new Bayesian inference package Infer.NET in terms of its capacity for statistical analyses. Infer.NET differs from the well-known BUGS Bayesian inference packages in that its main engine is the variational Bayes family of deterministic approximation algorithms rather than Markov chain Monte Carlo. The underlying rationale is that such deterministic algorithms can handle bigger problems due to their increased speed, despite some loss of accuracy. We find that Infer.NET is a well-designed computational framework and offers significant speed advantages over BUGS. Nevertheless, the current release is limited in terms of the breadth of models it can handle, and its inference is sometimes inaccurate. Supplemental materials accompany the online version of this article.
    Preview · Article · May 2011 · The American Statistician
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    José E. Chacón · Tarn Duong · M. P. Wand
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    ABSTRACT: We investigate general kernel density derivative estimators, that is, kernel estimators of multivariate density derivative functions using general (or unconstrained) bandwidth matrix selectors. These density derivative estimators have been relatively less well researched than their density estimator analogues. A major obstacle for progress has been the intractability of the matrix analysis when treating higher order multivariate derivatives. With an alternative vectorization of these higher order derivatives, these mathematical intractabilities are surmounted in an elegant and unified framework. The finite sample and asymptotic analysis of squared errors for density estimators are generalized to density derivative estimators. Moreover, we are able to exhibit a closed form expression for a normal scale bandwidth matrix for density derivative estimators. These normal scale bandwidths are employed in a numerical study to demonstrate the gain in performance of unconstrained selectors over their constrained counterparts.
    Preview · Article · Apr 2011 · Statistica Sinica
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    P. Hall · J. T. Ormerod · M. P. Wand
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    ABSTRACT: Likelihood-based inference for the parameters of generalized linear mixed models is hindered by the presence of intractable integrals. Gaussian variational approximation provides a fast and effective means of approximate inference. We provide some theory for this type of approximation for a simple Poisson mixed model. In particular, we establish consistency at rate m−1/2 + n−1, where m is the number of groups and n is the number of repeated measurements.
    Full-text · Article · Jan 2011 · Statistica Sinica
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    J. T. Ormerod · M. P. Wand
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    ABSTRACT: Variational approximation methods have become a mainstay of contemporary Machine Learning methodology, but currently have little presence in Statistics. We devise an effective variational approximation strategy for fitting generalized linear mixed models (GLMM) appropriate for grouped data. It involves Gaussian approximation to the distributions of random effects vectors, conditional on the responses. We show that Gaussian variational approximation is a relatively simple and natural alternative to Laplace approximation for fast, non-Monte Carlo, GLMM analysis. Numerical studies show Gaussian variational approximation to be very accurate in grouped data GLMM contexts. Finally, we point to some recent theory on consistency of Gaussian variational approximation in this context.
    Full-text · Article · Jan 2011 · Journal of Computational and Graphical Statistics
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    M. P. Wand · J. T. Ormerod
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    ABSTRACT: We introduce the concept of penalized wavelets to facilitate seamless embedding of wavelets into semiparametric regression models. In particular, we show that penalized wavelets are analogous to penalized splines; the latter being the established approach to function estimation in semiparametric regression. They differ only in the type of penalization that is appropriate. This fact is not borne out by the existing wavelet literature, where the regression modelling and fitting issues are overshadowed by computational issues such as efficiency gains afforded by the Discrete Wavelet Transform and partially obscured by a tendency to work in the wavelet coefficient space. With penalized wavelet structure in place, we then show that fitting and inference can be achieved via the same general approaches used for penalized splines: penalized least squares, maximum likelihood and best prediction within a frequentist mixed model framework, and Markov chain Monte Carlo and mean field variational Bayes within a Bayesian framework. Penalized wavelets are also shown have a close relationship with wide data (“p≫n”) regression and benefit from ongoing research on that topic.
    Full-text · Article · Jan 2011 · Electronic Journal of Statistics
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    Jennifer K. Marley · Matthew P. Wand
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    ABSTRACT: We provide several illustrations of Bayesian semiparametric regression analyses in the BRugs package. BRugs facilitates use of the BUGS inference engine from the R computing environment and allows analyses to be managed using scripts. The examples are chosen to represent an array of non-standard situations, for which mixed model software is not viable. The situations include: the response variable being outside of the one-parameter exponential family, data subject to missingness, data subject to measurement error and parameters entering the model via an index.
    Preview · Article · Nov 2010 · Journal of statistical software
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    R. J. Samworth · M. P. Wand
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    ABSTRACT: We study kernel estimation of highest-density regions (HDR). Our main contributions are two-fold. First, we derive a uniform-in-bandwidth asymptotic approximation to a risk that is appropriate for HDR estimation. This approximation is then used to derive a bandwidth selection rule for HDR estimation possessing attractive asymptotic properties. We also present the results of numerical studies that illustrate the benefits of our theory and methodology.
    Preview · Article · Oct 2010 · The Annals of Statistics
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    M Al Kadiri · R.J. Carroll · M.P. Wand
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    ABSTRACT: We study the marginal longitudinal nonparametric regression problem and some of its semiparametric extensions. We point out that, while several elaborate proposals for efficient estimation have been proposed, a relative simple and straightforward one, based on penalized splines, has not. After describing our approach, we then explain how Gibbs sampling and the BUGS software can be used to achieve quick and effective implementation. Illustrations are provided for nonparametric regression and additive models.
    Full-text · Article · Aug 2010 · Statistics [?] Probability Letters
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    J. T. Ormerod · M. P. Wand
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    ABSTRACT: Variational approximations facilitate approximate inference for the parameters in complex statistical models and provide fast, deterministic alternatives to Monte Carlo methods. However, much of the contemporary literature on variational approximations is in Computer Science rather than Statistics, and uses terminology, notation and examples from the former field. In this article we explain variational approximation in statistical terms. In particular, we illustrate the ideas of variational approximation using examples that are familiar to statisticians.
    Full-text · Article · May 2010 · The American Statistician

Publication Stats

6k Citations
194.24 Total Impact Points

Institutions

  • 2011-2014
    • University of Technology Sydney
      • School of Mathematical Sciences
      Sydney, New South Wales, Australia
    • French National Centre for Scientific Research
      Lutetia Parisorum, Île-de-France, France
  • 2008-2011
    • University of Wollongong
      • School of Mathematics and Applied Statistics (SMAS)
      City of Greater Wollongong, New South Wales, Australia
  • 1993-2008
    • University of New South Wales
      • • School of Mathematics and Statistics
      • • Department of Statistics
      • • Australian Graduate School of Management
      Kensington, New South Wales, Australia
    • McGill University
      • School of Computer Science
      Montréal, Quebec, Canada
  • 2001-2007
    • Harvard Medical School
      • Department of Medicine
      Boston, Massachusetts, United States
  • 1996-2004
    • Harvard University
      • Department of Biostatistics
      Cambridge, Massachusetts, United States
  • 2001-2003
    • Massachusetts Department of Public Health
      Boston, Massachusetts, United States
  • 1992-1993
    • Rice University
      • Department of Statistics
      Houston, Texas, United States