Results 1 - 10
of
267
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 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, ..."
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Cited by 4365 (92 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 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 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 large-scale 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 806 (10 self)
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Statistical applications in fields such as bioinformatics, information retrieval, speech processing, image processing and communications often involve large-scale 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 large-scale data analysis problems. We also present examples of graphical models in bioinformatics, error-control coding and language processing.
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 bio-sequence analysis, and KFMs have bee ..."
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Cited by 770 (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 bio-sequence 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) linear-Gaussian. 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 Rao-Blackwellised 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.
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 443 (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 Corr-LDA 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 held-out likelihood, automatic annotation, and text-based image retrieval using the Corel database of images and captions.
Implementing approximate Bayesian inference for latent Gaussian models using integrated nested Laplace approximations: A manual for the inla-program
, 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, smoothing-spline models, state-space models, semiparametric regression, spatial and spatio-temp ..."
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Cited by 294 (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, smoothing-spline models, state-space models, semiparametric regression, spatial and spatio-temporal models, log-Gaussian Cox-processes, 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 non-Gaussian response variables. The posterior marginals are not available in closed form due to the non-Gaussian 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
Variational inference for Dirichlet process mixtures
- Bayesian Analysis
, 2005
"... Abstract. Dirichlet process (DP) mixture models are the cornerstone of nonparametric Bayesian statistics, and the development of Monte-Carlo Markov chain (MCMC) sampling methods for DP mixtures has enabled the application of nonparametric Bayesian methods to a variety of practical data analysis prob ..."
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Cited by 244 (27 self)
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Abstract. Dirichlet process (DP) mixture models are the cornerstone of nonparametric Bayesian statistics, and the development of Monte-Carlo Markov chain (MCMC) sampling methods for DP mixtures has enabled the application of nonparametric Bayesian methods to a variety of practical data analysis problems. However, MCMC sampling can be prohibitively slow, and it is important to explore alternatives. One class of alternatives is provided by variational methods, a class of deterministic algorithms that convert inference problems into optimization problems (Opper and Saad 2001; Wainwright and Jordan 2003). Thus far, variational methods have mainly been explored in the parametric setting, in particular within the formalism of the exponential family (Attias 2000; Ghahramani and Beal 2001; Blei et al. 2003). In this paper, we present a variational inference algorithm for DP mixtures. We present experiments that compare the algorithm to Gibbs sampling algorithms for DP mixtures of Gaussians and present an application to a large-scale image analysis problem.
Online Learning for Latent Dirichlet Allocation
"... 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 collection ..."
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Cited by 209 (21 self)
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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 performance of online LDA in several ways, including by fitting a 100-topic topic model to 3.3M articles from Wikipedia in a single pass. We demonstrate that online LDA finds topic models as good or better than those found with batch VB, and in a fraction of the time. 1
Competitive Coevolution through Evolutionary Complexification
- Journal of Artificial Intelligence Research
, 2002
"... Two major goals in machine learning are the discovery of complex multidimensional solutions and continual improvement of existing solutions. In this paper, we argue that complexification, i.e. the incremental elaboration of solutions through adding new structure, achieves both these goals. We demons ..."
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Cited by 202 (71 self)
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Two major goals in machine learning are the discovery of complex multidimensional solutions and continual improvement of existing solutions. In this paper, we argue that complexification, i.e. the incremental elaboration of solutions through adding new structure, achieves both these goals. We demonstrate the power of complexification through the NeuroEvolution of Augmenting Topologies (NEAT) method, which evolves increasingly complex neural network architectures. NEAT is applied to an open-ended coevolutionary robot duel domain where robot controllers compete head to head. Because the robot duel domain supports a wide range of sophisticated strategies, and because coevolution benefits from an escalating arms race, it serves as a suitable testbed for observing the effect of evolving increasingly complex controllers. The result is an arms race of increasingly sophisticated strategies. When compared to the evolution of networks with fixed structure, complexifying networks discover significantly more sophisticated strategies. The results suggest that in order to realize the full potential of evolution, and search in general, solutions must be allowed to complexify as well as optimize.
Expectation-propagation for the generative aspect model
- in UAI-2000, Proceedings of the 18th Conference in Uncertainty in Artificial Intelligence
"... The generative aspect model is an extension of the multinomial model for text that allows word probabilities to vary stochastically across docu-ments. Previous results with aspect models have been promising, but hindered by the computa-tional difficulty of carrying out inference and learning. This p ..."
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Cited by 157 (5 self)
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The generative aspect model is an extension of the multinomial model for text that allows word probabilities to vary stochastically across docu-ments. Previous results with aspect models have been promising, but hindered by the computa-tional difficulty of carrying out inference and learning. This paper demonstrates that the sim-ple variational methods of Blei et al. (2001) can lead to inaccurate inferences and biased learning for the generative aspect model. We develop an alternative approach that leads to higher accuracy at comparable cost. An extension of Expectation-Propagation is used for inference and then em-bedded in an EM algorithm for learning. Exper-imental results are presented for both synthetic and real data sets. 1
Propagation Algorithms for Variational Bayesian Learning
- In Advances in Neural Information Processing Systems 13
, 2001
"... Variational approximations are becoming a widespread tool for Bayesian learning of graphical models. We provide some theoretical results for the variational updates in a very general family of conjugate-exponential graphical models. We show how the belief propagation and the junction tree algorithms ..."
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Cited by 139 (20 self)
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Variational approximations are becoming a widespread tool for Bayesian learning of graphical models. We provide some theoretical results for the variational updates in a very general family of conjugate-exponential graphical models. We show how the belief propagation and the junction tree algorithms can be used in the inference step of variational Bayesian learning. Applying these results to the Bayesian analysis of linear-Gaussian state-space models we obtain a learning procedure that exploits the Kalman smoothing propagation, while integrating over all model parameters. We demonstrate how this can be used to infer the hidden state dimensionality of the state-space model in a variety of synthetic problems and one real high-dimensional data set.
