Browsing by Author "Dunson, D"

Now showing 1 - 4 of 4
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    Approximations of Markov Chains and High-Dimensional Bayesian Inference
    (2015) Mattingly, JC; Johndrow, J; Mukherjee, S; Dunson, D
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    Bayesian crack detection in ultra high resolution multimodal images of paintings
    (2013 18th International Conference on Digital Signal Processing, DSP 2013, 2013-12-06) Cornelis, B; Yang, Y; Vogelstein, JT; Dooms, A; Daubechies, I; Dunson, D
    The preservation of our cultural heritage is of paramount importance. Thanks to recent developments in digital acquisition techniques, powerful image analysis algorithms are developed which can be useful non-invasive tools to assist in the restoration and preservation of art. In this paper we propose a semi-supervised crack detection method that can be used for high-dimensional acquisitions of paintings coming from different modalities. Our dataset consists of a recently acquired collection of images of the Ghent Altarpiece (1432), one of Northern Europe's most important art masterpieces. Our goal is to build a classifier that is able to discern crack pixels from the background consisting of non-crack pixels, making optimal use of the information that is provided by each modality. To accomplish this we employ a recently developed non-parametric Bayesian classifier, that uses tensor factorizations to characterize any conditional probability. A prior is placed on the parameters of the factorization such that every possible interaction between predictors is allowed while still identifying a sparse subset among these predictors. The proposed Bayesian classifier, which we will refer to as conditional Bayesian tensor factorization or CBTF, is assessed by visually comparing classification results with the Random Forest (RF) algorithm. © 2013 IEEE.
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    Dynamic nonparametric bayesian models for analysis of music
    (Journal of the American Statistical Association, 2010-06-01) Ren, L; Dunson, D; Lindroth, S; Carin, L
    The dynamic hierarchical Dirichlet process (dHDP) is developed to model complex sequential data, with a focus on audio signals from music. The music is represented in terms of a sequence of discrete observations, and the sequence is modeled using a hidden Markov model (HMM) with time-evolving parameters. The dHDP imposes the belief that observations that are temporally proximate are more likely to be drawn from HMMs with similar parameters, while also allowing for "innovation" associated with abrupt changes in the music texture. The sharing mechanisms of the time-evolving model are derived, and for inference a relatively simple Markov chain Monte Carlo sampler is developed. Segmentation of a given musical piece is constituted via the model inference. Detailed examples are presented on several pieces, with comparisons to other models. The dHDP results are also compared with a conventional music-theoretic analysis. All the supplemental materials used by this paper are available online. © 2010 American Statistical Association.
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    Lognormal and gamma mixed negative binomial regression
    (Proceedings of the 29th International Conference on Machine Learning, ICML 2012, 2012-10-10) Zhou, M; Li, L; Dunson, D; Carin, L
    In regression analysis of counts, a lack of simple and efficient algorithms for posterior computation has made Bayesian approaches appear unattractive and thus underdeveloped. We propose a lognormal and gamma mixed negative binomial (NB) regression model for counts, and present efficient closed-form Bayesian inference; unlike conventional Poisson models, the proposed approach has two free parameters to include two different kinds of random effects, and allows the incorporation of prior information, such as sparsity in the regression coefficients. By placing a gamma distribution prior on the NB dispersion parameter r, and connecting a log-normal distribution prior with the logit of the NB probability parameter p, efficient Gibbs sampling and variational Bayes inference are both developed. The closed-form updates are obtained by exploiting conditional conjugacy via both a compound Poisson representation and a Polya-Gamma distribution based data augmentation approach. The proposed Bayesian inference can be implemented routinely, while being easily generalizable to more complex settings involving multivariate dependence structures. The algorithms are illustrated using real examples. Copyright 2012 by the author(s)/owner(s).