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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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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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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
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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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 1 (1 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
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.
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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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