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13
Construction of dependent Dirichlet processes based on Poisson processes
 In NIPS
, 2010
"... We present a method for constructing dependent Dirichlet processes. The new approach exploits the intrinsic relationship between Dirichlet and Poisson processes in order to create a Markov chain of Dirichlet processes suitable for use as a prior over evolving mixture models. The method allows for t ..."
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Cited by 23 (1 self)
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We present a method for constructing dependent Dirichlet processes. The new approach exploits the intrinsic relationship between Dirichlet and Poisson processes in order to create a Markov chain of Dirichlet processes suitable for use as a prior over evolving mixture models. The method allows for the creation, removal, and location variation of component models over time while maintaining the property that the random measures are marginally DP distributed. Additionally, we derive a Gibbs sampling algorithm for model inference and test it on both synthetic and real data. Empirical results demonstrate that the approach is effective in estimating dynamically varying mixture models. 1
Spatial Normalized Gamma Processes
"... Dependent Dirichlet processes (DPs) are dependent sets of random measures, each being marginally DP distributed. They are used in Bayesian nonparametric models when the usual exchangeability assumption does not hold. We propose a simple and general framework to construct dependent DPs by marginalizi ..."
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Cited by 20 (3 self)
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Dependent Dirichlet processes (DPs) are dependent sets of random measures, each being marginally DP distributed. They are used in Bayesian nonparametric models when the usual exchangeability assumption does not hold. We propose a simple and general framework to construct dependent DPs by marginalizing and normalizing a single gamma process over an extended space. The result is a set of DPs, each associated with a point in a space such that neighbouring DPs are more dependent. We describe Markov chain Monte Carlo inference involving Gibbs sampling and three different MetropolisHastings proposals to speed up convergence. We report an empirical study of convergence on a synthetic dataset and demonstrate an application of the model to topic modeling through time. 1
Dynamic Nonparametric Bayesian Models for Analysis of Music
"... 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 timeevolving parame ..."
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Cited by 10 (4 self)
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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 timeevolving 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 timeevolving 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 musictheoretic analysis.
Distance Dependent Infinite Latent Feature Models
, 2011
"... Latent feature models are widely used to decompose data into a small number of components. Bayesian nonparametric variants of these models, which use the Indian buffet process (IBP) as a prior over latent features, allow the number of features to be determined from the data. We present a generalizat ..."
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Cited by 10 (0 self)
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Latent feature models are widely used to decompose data into a small number of components. Bayesian nonparametric variants of these models, which use the Indian buffet process (IBP) as a prior over latent features, allow the number of features to be determined from the data. We present a generalization of the IBP, the distance dependent Indian buffet process (ddIBP), for modeling nonexchangeable data. It relies on a distance function defined between data points, biasing nearby data to share more features. The choice of distance function allows for many kinds of dependencies, including temporal or spatial. Further, the original IBP is a special case of the ddIBP. In this paper, we develop the ddIBP and theoretically characterize the distribution of how features are shared between data. We derive a Markov chain Monte Carlo sampler for a linear Gaussian model with a ddIBP prior and study its performance on several data sets for which exchangeability is not a reasonable assumption.
Coupling nonparametric mixtures via latent Dirichlet processes
 In NIPS. 2012
"... Mixture distributions are often used to model complex data. In this paper, we develop a new method that jointly estimates mixture models over multiple data sets by exploiting the statistical dependencies between them. Specifically, we introduce a set of latent Dirichlet processes as sources of compo ..."
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Cited by 5 (0 self)
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Mixture distributions are often used to model complex data. In this paper, we develop a new method that jointly estimates mixture models over multiple data sets by exploiting the statistical dependencies between them. Specifically, we introduce a set of latent Dirichlet processes as sources of component models (atoms), and for each data set, we construct a nonparametric mixture model by combining subsampled versions of the latent DPs. Each mixture model may acquire atoms from different latent DPs, while each atom may be shared by multiple mixtures. This multitomulti association distinguishes the proposed method from previous ones that require the model structure to be a tree or a chain, allowing more flexible designs. We also derive a sampling algorithm that jointly infers the model parameters and present experiments on both document analysis and image modeling. 1
A survey of nonexchangeable priors for Bayesian nonparametric models
, 2014
"... Dependent nonparametric processes extend distributions over measures, such as the Dirichlet process and the beta process, to give distributions over collections of measures, typically indexed by values in some covariate space. Such models are appropriate priors when exchangeability assumptions do ..."
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Cited by 3 (0 self)
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Dependent nonparametric processes extend distributions over measures, such as the Dirichlet process and the beta process, to give distributions over collections of measures, typically indexed by values in some covariate space. Such models are appropriate priors when exchangeability assumptions do not hold, and instead we want our model to vary fluidly with some set of covariates. Since the concept of dependent nonparametric processes was formalized by MacEachern [1], there have been a number of models proposed and used in the statistics and machine learning literatures. Many of these models exhibit underlying similarities, an understanding of which, we hope, will help in selecting an appropriate prior, developing new models, and leveraging inference techniques.
Toward Versatile Structural Modification for Bayesian Nonparametric Time Series Models
 Sing Lee), School of Computer Science. Carnegie Mellon University
, 2010
"... Copyright c©2010 by Thomas Stepleton. This document is licensed under a Creative Commons ..."
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Cited by 2 (0 self)
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Copyright c©2010 by Thomas Stepleton. This document is licensed under a Creative Commons
A unifying representation for a class of dependent random measures
, 1211
"... We present a general construction for dependent random measures based on thinning Poisson processes on an augmented space. The framework is not restricted to dependent versions of a specific nonparametric model, but can be applied to all models that can be represented using completely random measure ..."
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We present a general construction for dependent random measures based on thinning Poisson processes on an augmented space. The framework is not restricted to dependent versions of a specific nonparametric model, but can be applied to all models that can be represented using completely random measures. Several existing dependent random measures can be seen as specific cases of this framework. Interesting properties of the resulting measures are derived and the efficacy of the framework is demonstrated by constructing a covariatedependent latent feature model and topic model that obtain superior predictive performance. 1