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Latent dirichlet allocation
 Journal of Machine Learning Research
, 2003
"... We describe latent Dirichlet allocation (LDA), a generative probabilistic model for collections of discrete data such as text corpora. LDA is a threelevel 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, ..."
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Cited by 4194 (91 self)
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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 threelevel 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 set of topic probabilities. In the context of text modeling, the topic probabilities provide an explicit representation of a document. We present efficient approximate inference techniques based on variational methods and an EM algorithm for empirical Bayes parameter estimation. We report results in document modeling, text classification, and collaborative filtering, comparing to a mixture of unigrams model and the probabilistic LSI model. 1.
Learning in graphical models
 STATISTICAL SCIENCE
, 2004
"... Statistical applications in fields such as bioinformatics, information retrieval, speech processing, image processing and communications often involve largescale models in which thousands or millions of random variables are linked in complex ways. Graphical models provide a general methodology for ..."
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Cited by 800 (10 self)
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Statistical applications in fields such as bioinformatics, information retrieval, speech processing, image processing and communications often involve largescale models in which thousands or millions of random variables are linked in complex ways. Graphical models provide a general methodology for approaching these problems, and indeed many of the models developed by researchers in these applied fields are instances of the general graphical model formalism. We review some of the basic ideas underlying graphical models, including the algorithmic ideas that allow graphical models to be deployed in largescale data analysis problems. We also present examples of graphical models in bioinformatics, errorcontrol coding and language processing.
Learning generative visual models from few training examples: an incremental Bayesian approach tested on 101 object categories
, 2004
"... Abstract — Current computational approaches to learning visual object categories require thousands of training images, are slow, cannot learn in an incremental manner and cannot incorporate prior information into the learning process. In addition, no algorithm presented in the literature has been te ..."
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Cited by 770 (17 self)
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Abstract — Current computational approaches to learning visual object categories require thousands of training images, are slow, cannot learn in an incremental manner and cannot incorporate prior information into the learning process. In addition, no algorithm presented in the literature has been tested on more than a handful of object categories. We present an method for learning object categories from just a few training images. It is quick and it uses prior information in a principled way. We test it on a dataset composed of images of objects belonging to 101 widely varied categories. Our proposed method is based on making use of prior information, assembled from (unrelated) object categories which were previously learnt. A generative probabilistic model is used, which represents the shape and appearance of a constellation of features belonging to the object. The parameters of the model are learnt incrementally in a Bayesian manner. Our incremental algorithm is compared experimentally to an earlier batch Bayesian algorithm, as well as to one based on maximumlikelihood. The incremental and batch versions have comparable classification performance on small training sets, but incremental learning is significantly faster, making realtime learning feasible. Both Bayesian methods outperform maximum likelihood on small training sets. I.
Dynamic Bayesian Networks: Representation, Inference and Learning
, 2002
"... Modelling sequential data is important in many areas of science and engineering. Hidden Markov models (HMMs) and Kalman filter models (KFMs) are popular for this because they are simple and flexible. For example, HMMs have been used for speech recognition and biosequence analysis, and KFMs have bee ..."
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Cited by 758 (3 self)
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Modelling sequential data is important in many areas of science and engineering. Hidden Markov models (HMMs) and Kalman filter models (KFMs) are popular for this because they are simple and flexible. For example, HMMs have been used for speech recognition and biosequence analysis, and KFMs have been used for problems ranging from tracking planes and missiles to predicting the economy. However, HMMs
and KFMs are limited in their “expressive power”. Dynamic Bayesian Networks (DBNs) generalize HMMs by allowing the state space to be represented in factored form, instead of as a single discrete random variable. DBNs generalize KFMs by allowing arbitrary probability distributions, not just (unimodal) linearGaussian. In this thesis, I will discuss how to represent many different kinds of models as DBNs, how to perform exact and approximate inference in DBNs, and how to learn DBN models from sequential data.
In particular, the main novel technical contributions of this thesis are as follows: a way of representing
Hierarchical HMMs as DBNs, which enables inference to be done in O(T) time instead of O(T 3), where T is the length of the sequence; an exact smoothing algorithm that takes O(log T) space instead of O(T); a simple way of using the junction tree algorithm for online inference in DBNs; new complexity bounds on exact online inference in DBNs; a new deterministic approximate inference algorithm called factored frontier; an analysis of the relationship between the BK algorithm and loopy belief propagation; a way of
applying RaoBlackwellised particle filtering to DBNs in general, and the SLAM (simultaneous localization
and mapping) problem in particular; a way of extending the structural EM algorithm to DBNs; and a variety of different applications of DBNs. However, perhaps the main value of the thesis is its catholic presentation of the field of sequential data modelling.
Constructing Free Energy Approximations and Generalized Belief Propagation Algorithms
 IEEE Transactions on Information Theory
, 2005
"... Important inference problems in statistical physics, computer vision, errorcorrecting coding theory, and artificial intelligence can all be reformulated as the computation of marginal probabilities on factor graphs. The belief propagation (BP) algorithm is an efficient way to solve these problems t ..."
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Cited by 586 (13 self)
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Important inference problems in statistical physics, computer vision, errorcorrecting coding theory, and artificial intelligence can all be reformulated as the computation of marginal probabilities on factor graphs. The belief propagation (BP) algorithm is an efficient way to solve these problems that is exact when the factor graph is a tree, but only approximate when the factor graph has cycles. We show that BP fixed points correspond to the stationary points of the Bethe approximation of the free energy for a factor graph. We explain how to obtain regionbased free energy approximations that improve the Bethe approximation, and corresponding generalized belief propagation (GBP) algorithms. We emphasize the conditions a free energy approximation must satisfy in order to be a “valid ” or “maxentnormal ” approximation. We describe the relationship between four different methods that can be used to generate valid approximations: the “Bethe method, ” the “junction graph method, ” the “cluster variation method, ” and the “region graph method.” Finally, we explain how to tell whether a regionbased approximation, and its corresponding GBP algorithm, is likely to be accurate, and describe empirical results showing that GBP can significantly outperform BP.
Belief Propagation
, 2010
"... When a pair of nuclearpowered Russian submarines was reported patrolling off the eastern seaboard of the U.S. last summer, Pentagon officials expressed wariness over the Kremlin’s motivations. At the same time, these officials emphasized their confidence in the U.S. Navy’s tracking capabilities: “W ..."
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Cited by 479 (11 self)
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When a pair of nuclearpowered Russian submarines was reported patrolling off the eastern seaboard of the U.S. last summer, Pentagon officials expressed wariness over the Kremlin’s motivations. At the same time, these officials emphasized their confidence in the U.S. Navy’s tracking capabilities: “We’ve known where they were,” a senior Defense Department official told the New York Times, “and we’re not concerned about our ability to track the subs.” While the official did not divulge the methods used by the Navy to track submarines, the Times added that such
Modeling annotated data
 IN PROC. OF THE 26TH INTL. ACM SIGIR CONFERENCE
, 2003
"... 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 that are aimed at such data, culminating in the Cor ..."
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Cited by 436 (12 self)
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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 that are aimed at such data, culminating in the CorrLDA model, a latent variable model that is effective at modeling the joint distribution of both types and the conditional distribution of the annotation given the primary type. We take an empirical Bayes approach to finding parameter estimates and conduct experiments in heldout likelihood, automatic annotation, and textbased image retrieval using the Corel database of images and captions.
A family of algorithms for approximate Bayesian inference
, 2001
"... One of the major obstacles to using Bayesian methods for pattern recognition has been its computational expense. This thesis presents an approximation technique that can perform Bayesian inference faster and more accurately than previously possible. This method, "Expectation Propagation," ..."
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Cited by 369 (11 self)
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One of the major obstacles to using Bayesian methods for pattern recognition has been its computational expense. This thesis presents an approximation technique that can perform Bayesian inference faster and more accurately than previously possible. This method, "Expectation Propagation," unifies and generalizes two previous techniques: assumeddensity filtering, an extension of the Kalman filter, and loopy belief propagation, an extension of belief propagation in Bayesian networks. The unification shows how both of these algorithms can be viewed as approximating the true posterior distribution with a simpler distribution, which is close in the sense of KLdivergence. Expectation Propagation exploits the best of both algorithms: the generality of assumeddensity filtering and the accuracy of loopy belief propagation. Loopy belief propagation, because it propagates exact belief states, is useful for limited types of belief networks, such as purely discrete networks. Expectation Propagati...
Mixed membership stochastic block models for relational data with application to proteinprotein interactions
 In Proceedings of the International Biometrics Society Annual Meeting
, 2006
"... We develop a model for examining data that consists of pairwise measurements, for example, presence or absence of links between pairs of objects. Examples include protein interactions and gene regulatory networks, collections of authorrecipient email, and social networks. Analyzing such data with p ..."
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Cited by 366 (51 self)
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We develop a model for examining data that consists of pairwise measurements, for example, presence or absence of links between pairs of objects. Examples include protein interactions and gene regulatory networks, collections of authorrecipient email, and social networks. Analyzing such data with probabilistic models requires special assumptions, since the usual independence or exchangeability assumptions no longer hold. We introduce a class of latent variable models for pairwise measurements: mixed membership stochastic blockmodels. Models in this class combine a global model of dense patches of connectivity (blockmodel) and a local model to instantiate nodespecific variability in the connections (mixed membership). We develop a general variational inference algorithm for fast approximate posterior inference. We demonstrate the advantages of mixed membership stochastic blockmodels with applications to social networks and protein interaction networks.