Results 1  10
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18
Nonparametric Factor Analysis with Beta Process Priors
"... We propose a nonparametric extension to the factor analysis problem using a beta process prior. This beta process factor analysis (BPFA) model allows for a dataset to be decomposed into a linear combination of a sparse set of factors, providing information on the underlying structure of the observa ..."
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Cited by 80 (26 self)
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We propose a nonparametric extension to the factor analysis problem using a beta process prior. This beta process factor analysis (BPFA) model allows for a dataset to be decomposed into a linear combination of a sparse set of factors, providing information on the underlying structure of the observations. As with the Dirichlet process, the beta process is a fully Bayesian conjugate prior, which allows for analytical posterior calculation and straightforward inference. We derive a variational Bayes inference algorithm and demonstrate the model on the MNIST digits and HGDPCEPH cell line panel datasets. 1.
Betanegative binomial process and Poisson factor analysis
 In AISTATS
, 2012
"... A betanegative binomial (BNB) process is proposed, leading to a betagammaPoisson process, which may be viewed as a “multiscoop” generalization of the betaBernoulli process. The BNB process is augmented into a betagammagammaPoisson hierarchical structure, and applied as a nonparametric Bayesia ..."
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Cited by 22 (9 self)
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A betanegative binomial (BNB) process is proposed, leading to a betagammaPoisson process, which may be viewed as a “multiscoop” generalization of the betaBernoulli process. The BNB process is augmented into a betagammagammaPoisson hierarchical structure, and applied as a nonparametric Bayesian prior for an infinite Poisson factor analysis model. A finite approximation for the beta process Lévy random measure is constructed for convenient implementation. Efficient MCMC computations are performed with data augmentation and marginalization techniques. Encouraging results are shown on document count matrix factorization. 1
Combinatorial clustering and the beta negative binomial process. arXiv preprint arXiv:1111.1802
, 2013
"... Abstract—We develop a Bayesian nonparametric approach to a general family of latent class problems in which individuals can belong simultaneously to multiple classes and where each class can be exhibited multiple times by an individual. We introduce a combinatorial stochastic process known as the ne ..."
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Cited by 16 (4 self)
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Abstract—We develop a Bayesian nonparametric approach to a general family of latent class problems in which individuals can belong simultaneously to multiple classes and where each class can be exhibited multiple times by an individual. We introduce a combinatorial stochastic process known as the negative binomial process (NBP) as an infinitedimensional prior appropriate for such problems. We show that the NBP is conjugate to the beta process, and we characterize the posterior distribution under the betanegative binomial process (BNBP) and hierarchical models based on the BNBP (the HBNBP). We study the asymptotic properties of the BNBP and develop a threeparameter extension of the BNBP that exhibits powerlaw behavior. We derive MCMC algorithms for posterior inference under the HBNBP, and we present experiments using these algorithms in the domains of image segmentation, object recognition, and document analysis.
Variational Inference for StickBreaking Beta Process Priors
"... We present a variational Bayesian inference algorithm for the stickbreaking construction of the beta process. We derive an alternate representation of the beta process that is amenable to variational inference, and present a bound relating the truncated beta process to its infinite counterpart. We ..."
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Cited by 9 (3 self)
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We present a variational Bayesian inference algorithm for the stickbreaking construction of the beta process. We derive an alternate representation of the beta process that is amenable to variational inference, and present a bound relating the truncated beta process to its infinite counterpart. We assess performance on two matrix factorization problems, using a nonnegative factorization model and a linearGaussian model. 1.
StickBreaking Beta Processes and the Poisson Process
"... We show that the stickbreaking construction of the beta process due to Paisley et al. (2010) can be obtained from the characterization of the beta process as a Poisson process. Specifically, we show that the mean measure of the underlying Poisson process is equal to that of the beta process. We use ..."
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Cited by 8 (5 self)
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We show that the stickbreaking construction of the beta process due to Paisley et al. (2010) can be obtained from the characterization of the beta process as a Poisson process. Specifically, we show that the mean measure of the underlying Poisson process is equal to that of the beta process. We use this underlying representation to derive error bounds on truncated beta processes that are tighter than those in the literature. We also develop a new MCMC inference algorithm for beta processes, based in part on our new Poisson process construction. 1
The combinatorial structure of beta negative binomial processes. arXiv:1401.0062
, 2013
"... ar ..."
Cluster and Feature Modeling from Combinatorial Stochastic Processes
"... Abstract. One of the focal points of the modern literature on Bayesian nonparametrics has been the problem of clustering, orpartitioning, where each data point is modeled as being associated with one and only one of some collection of groups called clusters or partition blocks. Underlying these Baye ..."
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Cited by 3 (1 self)
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Abstract. One of the focal points of the modern literature on Bayesian nonparametrics has been the problem of clustering, orpartitioning, where each data point is modeled as being associated with one and only one of some collection of groups called clusters or partition blocks. Underlying these Bayesian nonparametric models are a set of interrelated stochastic processes, most notably the Dirichlet process and the Chinese restaurant process. In this paper we provide a formal development of an analogous problem, called feature modeling, for associating data points with arbitrary nonnegative integer numbers of groups, now called features or topics. We review the existing combinatorial stochastic process representations for the clustering problem and develop analogous representations for the feature modeling problem. These representations include the beta process and the Indian buffet process as well as new representations that provide insight into the connections between these processes. We thereby bring the same level of completeness to the treatment of Bayesian nonparametric feature modeling that has previously been achieved for Bayesian nonparametric clustering.
Automatically Determining a Proper Length for Multidocument Summarization: A Bayesian Nonparametric Approach
"... Document summarization is an important task in the area of natural language processing, which aims to extract the most important information from a single document or a cluster of documents. In various summarization tasks, the summary length is manually defined. However, how to find the proper su ..."
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Cited by 1 (0 self)
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Document summarization is an important task in the area of natural language processing, which aims to extract the most important information from a single document or a cluster of documents. In various summarization tasks, the summary length is manually defined. However, how to find the proper summary length is quite a problem; and keeping all summaries restricted to the same length is not always a good choice. It is obviously improper to generate summaries with the same length for two clusters of documents which contain quite different quantity of information. In this paper, we propose a Bayesian nonparametric model for multidocument summarization in order to automatically determine the proper lengths of summaries. Assuming that an original document can be reconstructed from its summary, we describe the ”reconstruction ” by a Bayesian framework which selects sentences to form a good summary. Experimental results on DUC2004 data sets and some expanded data demonstrate the good quality of our summaries and the rationality of the length determination. 1
Mixture models with a prior on the number of components. arXiv:1502.06241
, 2015
"... A natural Bayesian approach for mixture models with an unknown number of components is to take the usual finite mixture model with symmetric Dirichlet weights, and put a prior on the number of components—that is, to use a mixture of finite mixtures (MFM). The most commonlyused method of inference ..."
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A natural Bayesian approach for mixture models with an unknown number of components is to take the usual finite mixture model with symmetric Dirichlet weights, and put a prior on the number of components—that is, to use a mixture of finite mixtures (MFM). The most commonlyused method of inference for MFMs is reversible jump Markov chain Monte Carlo, but it can be nontrivial to design good reversible jump moves, especially in highdimensional spaces. Meanwhile, there are samplers for Dirichlet process mixture (DPM) models that are relatively simple and are easily adapted to new applications. It turns out that, in fact, many of the essential properties of DPMs are also exhibited by MFMs—an exchangeable partition distribution, restaurant process, random measure representation, and stickbreaking representation—and crucially, the MFM analogues are simple enough that they can be used much like the corresponding DPM properties. Consequently, many of the powerful methods developed for inference in DPMs can be directly applied to MFMs as well; this simplifies the implementation of MFMs and can substantially improve mixing. We illustrate with real and simulated data, including highdimensional gene expression data used to discriminate cancer subtypes.
Declaration
, 2011
"... The attached document may provide the author's accepted version of a published work. ..."
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The attached document may provide the author's accepted version of a published work.