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Hierarchical beta processes and the Indian buffet process. This volume
 In Practical Nonparametric and Semiparametric Bayesian Statistics
, 2007
"... We show that the beta process is the de Finetti mixing distribution underlying the Indian buffet process of [2]. This result shows that the beta process plays the role for the Indian buffet process that the Dirichlet process plays for Chinese restaurant process, a parallel that guides us in deriving ..."
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Cited by 74 (14 self)
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We show that the beta process is the de Finetti mixing distribution underlying the Indian buffet process of [2]. This result shows that the beta process plays the role for the Indian buffet process that the Dirichlet process plays for Chinese restaurant process, a parallel that guides us in deriving analogs for the beta process of the many known extensions of the Dirichlet process. In particular we define Bayesian hierarchies of beta processes and use the connection to the beta process to develop posterior inference algorithms for the Indian buffet process. We also present an application to document classification, exploring a relationship between the hierarchical beta process and smoothed naive Bayes models. 1 1
Stickbreaking construction for the Indian buffet process
 In Proceedings of the International Conference on Artificial Intelligence and Statistics
"... The Indian buffet process (IBP) is a Bayesian nonparametric distribution whereby objects are modelled using an unbounded number of latent features. In this paper we derive a stickbreaking representation for the IBP. Based on this new representation, we develop slice samplers for the IBP that are ef ..."
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Cited by 46 (8 self)
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The Indian buffet process (IBP) is a Bayesian nonparametric distribution whereby objects are modelled using an unbounded number of latent features. In this paper we derive a stickbreaking representation for the IBP. Based on this new representation, we develop slice samplers for the IBP that are efficient, easy to implement and are more generally applicable than the currently available Gibbs sampler. This representation, along with the work of Thibaux and Jordan [17], also illuminates interesting theoretical connections between the IBP, Chinese restaurant processes, Beta processes and Dirichlet processes. 1
Indian Buffet Processes with Powerlaw Behavior
"... The Indian buffet process (IBP) is an exchangeable distribution over binary matrices used in Bayesian nonparametric featural models. In this paper we propose a threeparameter generalization of the IBP exhibiting powerlaw behavior. We achieve this by generalizing the beta process (the de Finetti me ..."
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Cited by 12 (0 self)
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The Indian buffet process (IBP) is an exchangeable distribution over binary matrices used in Bayesian nonparametric featural models. In this paper we propose a threeparameter generalization of the IBP exhibiting powerlaw behavior. We achieve this by generalizing the beta process (the de Finetti measure of the IBP) to the stablebeta process and deriving the IBP corresponding to it. We find interesting relationships between the stablebeta process and the PitmanYor process (another stochastic process used in Bayesian nonparametric models with interesting powerlaw properties). We derive a stickbreaking construction for the stablebeta process, and find that our powerlaw IBP is a good model for word occurrences in document corpora. 1
Nonparametric models for proteomic peak identification and quantification. Bayesian Inference for Gene Expression and Proteomics
, 2006
"... We present modelbased inference for proteomic peak identification and quantification from mass spectroscopy data, focusing on nonparametric Bayesian models. Using experimental data generated from MALDITOF mass spectroscopy (Matrix Assisted Laser Desorption Ionization Time of Flight) we model obser ..."
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Cited by 5 (2 self)
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We present modelbased inference for proteomic peak identification and quantification from mass spectroscopy data, focusing on nonparametric Bayesian models. Using experimental data generated from MALDITOF mass spectroscopy (Matrix Assisted Laser Desorption Ionization Time of Flight) we model observed intensities in spectra with a hierarchical nonparametric model for expected intensity as a function of timeofflight. We express the unknown intensity function as a sum of kernel functions, a natural choice of basis functions for modelling spectral peaks. We discuss how to place prior distributions on the unknown functions using Lévy random fields and describe posterior inference via a reversible jump Markov chain Monte Carlo algorithm.
A stickbreaking construction of the beta process (Technical Report
, 2009
"... We present and derive a new stickbreaking construction of the beta process. The construction is closely related to a special case of the stickbreaking construction of the Dirichlet process (Sethuraman, 1994) applied to the beta distribution. We derive an inference procedure that relies on Monte Ca ..."
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Cited by 5 (4 self)
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We present and derive a new stickbreaking construction of the beta process. The construction is closely related to a special case of the stickbreaking construction of the Dirichlet process (Sethuraman, 1994) applied to the beta distribution. We derive an inference procedure that relies on Monte Carlo integration to reduce the number of parameters to be inferred, and present results on synthetic data, the MNIST handwritten digits data set and a timeevolving gene expression data set. 1.
Nonparametric Bayesian Data Analysis
"... We review the current state of nonparametric Bayesian inference. The discussion follows a list of important statistical inference problems, including density estimation, regression, survival analysis, hierarchical models and model validation. For each inference problem we review relevant nonparametr ..."
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Cited by 3 (0 self)
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We review the current state of nonparametric Bayesian inference. The discussion follows a list of important statistical inference problems, including density estimation, regression, survival analysis, hierarchical models and model validation. For each inference problem we review relevant nonparametric Bayesian models and approaches including Dirichlet process (DP) models and variations, Polya trees, wavelet based models, neural network models, spline regression, CART, dependent DP models, and model validation with DP and Polya tree extensions of parametric models. 1
FUNCTION ESTIMATION, TIME SERIES MODELING AND SPATIOTEMPORAL MODELING
"... In this dissertation, we propose a new class of Bayesian method for nonparametric function estimation. We denote the new model as Lévy adaptive regression kernel or “LARK”. The LARK model is based on a stochastic expansion of functions in an overcomplete dictionary, which can be formulated as a stoc ..."
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In this dissertation, we propose a new class of Bayesian method for nonparametric function estimation. We denote the new model as Lévy adaptive regression kernel or “LARK”. The LARK model is based on a stochastic expansion of functions in an overcomplete dictionary, which can be formulated as a stochastic integration problem with a random measure. The unknown function is represented as a weighted sum of kernel or generator functions with arbitrary location parameters. Scaling parameters of the kernels are also taken as location specific and thus are adaptive, as with wavelets bases and dictionaries. Lévy random fields are introduced to construct prior distributions on the unknown functions, which lead to the specification of a joint prior distribution for the number of kernels, kernel regression coefficients and kernel associated parameters. Under Gaussian errors, the problem may be formulated as a sparse regression problem, with regularization induced through the Lévy random field prior. To make posterior inference on the unknown functions, a reversible
Romain Jean ThibauxAbstract
"... personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. To copy otherwise, to republish, to post on servers or to redistribute to lists, requires pri ..."
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personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. To copy otherwise, to republish, to post on servers or to redistribute to lists, requires prior specific