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We describe latent Dirichlet allocation (LDA), a generative probabilistic model for collections of discrete data such as text corpora. LDA is a three-level hierarchical Bayesian model, in which each item of a collection is modeled as a finite mixture over an underlying set of topics. Each topic is, in turn, modeled as an infinite mixture over an underlying… (More)

- Yee Whye Teh, Michael I. Jordan, Matthew J Beal, David M Blei, Qiang Fu
- 2003

a grant from Darpa in support of the CALO program. The authors wish to acknowledge helpful discussions with Lancelot James and Jim Pitman and the referees for useful comments. Abstract We consider problems involving groups of data, where each observation within a group is a draw from a mixture model, and where it is desirable to share mixture components… (More)

We consider the problem of modeling annotated data---data with multiple types where the instance of one type (such as a caption) serves as a description of the other type (such as an image). We describe three hierarchical probabilistic mixture models which aim to describe such data, culminating in <i>correspondence latent Dirichlet allocation</i>, a latent… (More)

We develop an online variational Bayes (VB) algorithm for Latent Dirichlet Allocation (LDA). Online LDA is based on online stochastic optimization with a natural gradient step, which we show converges to a local optimum of the VB objective function. It can handily analyze massive document collections, including those arriving in a stream. We study the… (More)

Observations consisting of measurements on relationships for pairs of objects arise in many settings, such as protein interaction and gene regulatory networks, collections of author-recipient email, and social networks. Analyzing such data with probabilisic models can be delicate because the simple exchangeability assumptions underlying many boilerplate… (More)

We introduce supervised latent Dirichlet allocation (sLDA), a statistical model of labelled documents. The model accommodates a variety of response types. We derive a maximum-likelihood procedure for parameter estimation, which relies on variational approximations to handle intractable posterior expectations. Prediction problems motivate this research: we… (More)

We address the problem of learning topic hierarchies from data. The model selection problem in this domain is daunting—which of the large collection of possible trees to use? We take a Bayesian approach, generating an appropriate prior via a distribution on partitions that we refer to as the nested Chinese restaurant process. This nonparametric prior allows… (More)

We derive a stochastic optimization algorithm for mean field variational inference, which we call online variational inference. Our algorithm approximates the posterior distribution of a probabilistic model with hidden variables, and can handle large (or even streaming) data sets of observations. Let x = x 1:n be n observations, β be global hidden… (More)

A family of probabilistic time series models is developed to analyze the time evolution of topics in large document collections. The approach is to use state space models on the natural parameters of the multinomial distributions that represent the topics. Variational approximations based on Kalman filters and nonparametric wavelet regression are developed… (More)