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793
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.
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.
Learning lowlevel vision
 International Journal of Computer Vision
, 2000
"... We show a learningbased method for lowlevel vision problems. We setup a Markov network of patches of the image and the underlying scene. A factorization approximation allows us to easily learn the parameters of the Markov network from synthetic examples of image/scene pairs, and to e ciently prop ..."
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Cited by 586 (31 self)
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We show a learningbased method for lowlevel vision problems. We setup a Markov network of patches of the image and the underlying scene. A factorization approximation allows us to easily learn the parameters of the Markov network from synthetic examples of image/scene pairs, and to e ciently propagate image information. Monte Carlo simulations justify this approximation. We apply this to the \superresolution &quot; problem (estimating high frequency details from a lowresolution image), showing good results. For the motion estimation problem, we show resolution of the aperture problem and llingin arising from application of the same probabilistic machinery.
Stereo matching using belief propagation
, 2003
"... In this paper, we formulate the stereo matching problem as a Markov network and solve it using Bayesian belief propagation. The stereo Markov network consists of three coupled Markov random fields that model the following: a smooth field for depth/disparity, a line process for depth discontinuity, ..."
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Cited by 348 (3 self)
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In this paper, we formulate the stereo matching problem as a Markov network and solve it using Bayesian belief propagation. The stereo Markov network consists of three coupled Markov random fields that model the following: a smooth field for depth/disparity, a line process for depth discontinuity, and a binary process for occlusion. After eliminating the line process and the binary process by introducing two robust functions, we apply the belief propagation algorithm to obtain the maximum a posteriori (MAP) estimation in the Markov network. Other lowlevel visual cues (e.g., image segmentation) can also be easily incorporated in our stereo model to obtain better stereo results. Experiments demonstrate that our methods are comparable to the stateoftheart stereo algorithms for many test cases.
Implementing approximate Bayesian inference for latent Gaussian models using integrated nested Laplace approximations: A manual for the inlaprogram
, 2008
"... Structured additive regression models are perhaps the most commonly used class of models in statistical applications. It includes, among others, (generalised) linear models, (generalised) additive models, smoothingspline models, statespace models, semiparametric regression, spatial and spatiotemp ..."
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Cited by 293 (20 self)
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Structured additive regression models are perhaps the most commonly used class of models in statistical applications. It includes, among others, (generalised) linear models, (generalised) additive models, smoothingspline models, statespace models, semiparametric regression, spatial and spatiotemporal models, logGaussian Coxprocesses, geostatistical and geoadditive models. In this paper we consider approximate Bayesian inference in a popular subset of structured additive regression models, latent Gaussian models, where the latent field is Gaussian, controlled by a few hyperparameters and with nonGaussian response variables. The posterior marginals are not available in closed form due to the nonGaussian response variables. For such models, Markov chain Monte Carlo methods can be implemented, but they are not without problems, both in terms of convergence and computational time. In some practical applications, the extent of these problems is such that Markov chain Monte Carlo is simply not an appropriate tool for routine analysis. We show that, by using an integrated nested Laplace approximation and its simplified version, we can directly compute very accurate approximations to the posterior marginals. The main benefit of these approximations
A theory of causal learning in children: Causal maps and Bayes nets
 PSYCHOLOGICAL REVIEW
, 2004
"... The authors outline a cognitive and computational account of causal learning in children. They propose that children use specialized cognitive systems that allow them to recover an accurate “causal map ” of the world: an abstract, coherent, learned representation of the causal relations among events ..."
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Cited by 243 (47 self)
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The authors outline a cognitive and computational account of causal learning in children. They propose that children use specialized cognitive systems that allow them to recover an accurate “causal map ” of the world: an abstract, coherent, learned representation of the causal relations among events. This kind of knowledge can be perspicuously understood in terms of the formalism of directed graphical causal models, or Bayes nets. Children’s causal learning and inference may involve computations similar to those for learning causal Bayes nets and for predicting with them. Experimental results suggest that 2to 4yearold children construct new causal maps and that their learning is consistent with the Bayes net formalism.
The Bayes Net Toolbox for MATLAB
 Computing Science and Statistics
, 2001
"... The Bayes Net Toolbox (BNT) is an opensource Matlab package for directed graphical models. BNT supports many kinds of nodes (probability distributions), exact and approximate inference, parameter and structure learning, and static and dynamic models. BNT is widely used in teaching and research: the ..."
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Cited by 243 (1 self)
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The Bayes Net Toolbox (BNT) is an opensource Matlab package for directed graphical models. BNT supports many kinds of nodes (probability distributions), exact and approximate inference, parameter and structure learning, and static and dynamic models. BNT is widely used in teaching and research: the web page has received over 28,000 hits since May 2000. In this paper, we discuss a broad spectrum of issues related to graphical models (directed and undirected), and describe, at a highlevel, how BNT was designed to cope with them all. We also compare BNT to other software packages for graphical models, and to the nascent OpenBayes effort.
Machine recognition of human activities: A survey
, 2008
"... The past decade has witnessed a rapid proliferation of video cameras in all walks of life and has resulted in a tremendous explosion of video content. Several applications such as contentbased video annotation and retrieval, highlight extraction and video summarization require recognition of the a ..."
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Cited by 213 (0 self)
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The past decade has witnessed a rapid proliferation of video cameras in all walks of life and has resulted in a tremendous explosion of video content. Several applications such as contentbased video annotation and retrieval, highlight extraction and video summarization require recognition of the activities occurring in the video. The analysis of human activities in videos is an area with increasingly important consequences from security and surveillance to entertainment and personal archiving. Several challenges at various levels of processing—robustness against errors in lowlevel processing, view and rateinvariant representations at midlevel processing and semantic representation of human activities at higher level processing—make this problem hard to solve. In this review paper, we present a comprehensive survey of efforts in the past couple of decades to address the problems of representation, recognition, and learning of human activities from video and related applications. We discuss the problem at two major levels of complexity: 1) “actions ” and 2) “activities. ” “Actions ” are characterized by simple motion patterns typically executed by a single human. “Activities ” are more complex and involve coordinated actions among a small number of humans. We will discuss several approaches and classify them according to their ability to handle varying degrees of complexity as interpreted above. We begin with a discussion of approaches to model the simplest of action classes known as atomic or primitive actions that do not require sophisticated dynamical modeling. Then, methods to model actions with more complex dynamics are discussed. The discussion then leads naturally to methods for higher level representation of complex activities.
Collaborative filtering with privacy via factor analysis
 In Proceedings of the 25th annual international ACM SIGIR conference on Research and development in information retrieval
, 2002
"... Collaborative filtering is valuable in ecommerce, and for direct recommendations for music, movies, news etc. But today’s systems use centralized databases and have several disadvantages, including privacy risks. As we move toward ubiquitous computing, there is a great potential for individuals to ..."
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Cited by 198 (9 self)
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Collaborative filtering is valuable in ecommerce, and for direct recommendations for music, movies, news etc. But today’s systems use centralized databases and have several disadvantages, including privacy risks. As we move toward ubiquitous computing, there is a great potential for individuals to share all kinds of information about places and things to do, see and buy, but the privacy risks are severe. In this paper we introduce a peertopeer protocol for collaborative filtering which protects the privacy of individual data. A second contribution of this paper is a new collaborative filtering algorithm based on factor analysis which appears to be the most accurate method for CF to date. The new algorithm has other advantages in speed and storage over previous algorithms. It is based on a careful probabilistic model of user choice, and on a probabilistically sound approach to dealing with missing data. Our experiments on several test datasets show that the algorithm is more accurate than previously reported methods, and the improvements increase with the sparseness of the dataset. Finally, factor analysis with privacy is applicable to other kinds of statistical analyses of survey or questionaire data scientists (e.g. web surveys or questionaires).