Results 1  10
of
21
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 2350 (63 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.
Symmetry analysis of reversible markov chains
 Internet Mathematics
, 2005
"... We show how to use subgroups of the symmetry group of a reversible Markov chain to give useful bounds on eigenvalues and their multiplicity. We supplement classical representation theoretic tools involving a group commuting with a selfadjoint operator with criteria for an eigenvector to descend to ..."
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Cited by 33 (11 self)
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We show how to use subgroups of the symmetry group of a reversible Markov chain to give useful bounds on eigenvalues and their multiplicity. We supplement classical representation theoretic tools involving a group commuting with a selfadjoint operator with criteria for an eigenvector to descend to an orbit graph. As examples, we show that the Metropolis construction can dominate a maxdegree construction by an arbitrary amount and that, in turn, the fastest mixing Markov chain can dominate the Metropolis construction by an arbitrary amount. 1
The interplay of bayesian and frequentist analysis
 Statist. Sci
, 2004
"... Statistics has struggled for nearly a century over the issue of whether the Bayesian or frequentist paradigm is superior. This debate is far from over and, indeed, should continue, since there are fundamental philosophical and pedagogical issues at stake. At the methodological level, however, the fi ..."
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Cited by 27 (0 self)
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Statistics has struggled for nearly a century over the issue of whether the Bayesian or frequentist paradigm is superior. This debate is far from over and, indeed, should continue, since there are fundamental philosophical and pedagogical issues at stake. At the methodological level, however, the fight has become considerably muted, with the recognition that each approach has a great deal to contribute to statistical practice and each is actually essential for full development of the other approach. In this article, we embark upon a rather idiosyncratic walk through some of these issues. Key words and phrases: Admissibility; Bayesian model checking; conditional frequentist; confidence intervals; consistency; coverage; design; hierarchical models; nonparametric
Computational Aspects of Nonparametric Bayesian Analysis with Applications to the Modeling of Multiple Binary Sequences
 Journal of Computational and Graphical Statistics
, 1998
"... We consider Markov mixture models for multiple longitudinal binary sequences. Prior uncertainty in the mixing distribution is characterized by a Dirichlet process centered on a matrix beta measure. We use this setting to evaluate and compare the performance of three competing algorithms which arise ..."
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Cited by 12 (2 self)
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We consider Markov mixture models for multiple longitudinal binary sequences. Prior uncertainty in the mixing distribution is characterized by a Dirichlet process centered on a matrix beta measure. We use this setting to evaluate and compare the performance of three competing algorithms which arise more generally in Dirichlet process mixture calculations: sequential imputations, Gibbs sampling, and a predictive recursion, for which an extension of the sequential calculations is introduced. This facilitates the estimation of quantities related to clustering structure which is not available in the original formulation. A numerical comparison is carried out in three examples. Our findings suggest that the sequential imputations method is most useful for relatively small problems, and that the predictive recursion can be an efficient preliminary tool for more reliable, but computationally intensive, Gibbs sampling implementations. Keywords: Dirichlet Process, Gibbs sampling, Partial Excha...
Generalizations of Polya’s urn problem
 Annals of Combinatorics
, 2003
"... Abstract. We consider generalizations of the classical Polya urn problem: Given finitely many bins each containing one ball, suppose that additional balls arrive one at a time. For each new ball, with probability p, create a new bin and place the ball in that bin; with probability 1 − p, place the b ..."
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Cited by 11 (1 self)
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Abstract. We consider generalizations of the classical Polya urn problem: Given finitely many bins each containing one ball, suppose that additional balls arrive one at a time. For each new ball, with probability p, create a new bin and place the ball in that bin; with probability 1 − p, place the ball in an existing bin, such that the probability the ball is placed in a bin is proportional to m γ,wheremis the number of balls in that bin. For p = 0, the number of bins is fixed and finite, and the behavior of the process depends on whether γ is greater than, equal to, or less than 1. We survey the known results and give new proofs for all three cases. We then consider the case p>0. When γ = 1, this is equivalent to the socalled preferential attachment scheme which leads to power law distribution for bin sizes. When γ>1, we prove that a single bin dominates, i.e., as the number of balls goes to infinity, the probability converges to 1 that any new ball either goes into that bin or creates a new bin. When p>0andγ<1, we show that under the assumption that certain limits exist, the fraction of bins having m balls shrinks exponentially as a function of m. We then discuss further generalizations and pose several open problems.
Is Bayesian Imitation Learning the Route to Believable Gamebots?
 In: Proc. GAMEON North America. (2005) 3–9
, 2005
"... As it strives to imitate observably successful actions, imitation learning allows for a quick acquisition of proven behaviors. Recent work from psychology and robotics suggests that Bayesian probability theory provides a mathematical framework for imitation learning. In this paper, we investigate th ..."
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Cited by 9 (3 self)
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As it strives to imitate observably successful actions, imitation learning allows for a quick acquisition of proven behaviors. Recent work from psychology and robotics suggests that Bayesian probability theory provides a mathematical framework for imitation learning. In this paper, we investigate the use of Bayesian imitation learning in realizing more lifelike computer game characters. Following our general strategy of analyzing the network traffic of multiplayer online games, we will present experiments in automatic imitation of behaviors contained in human generated data. Our results show that the Bayesian framework indeed leads to game agent behavior that appears very much humanlike.
Edgereinforced random walk on a ladder
 Ann. Probab
, 2005
"... We prove that the edgereinforced random walk on the ladder Z × {1,2} with initial weights a> 3/4 is recurrent. The proof uses a known representation of the edgereinforced random walk on a finite piece of the ladder as a random walk in a random environment. This environment is given by a marginal o ..."
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Cited by 8 (0 self)
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We prove that the edgereinforced random walk on the ladder Z × {1,2} with initial weights a> 3/4 is recurrent. The proof uses a known representation of the edgereinforced random walk on a finite piece of the ladder as a random walk in a random environment. This environment is given by a marginal of a multicomponent Gibbsian process. A transfer operator technique and entropy estimates from statistical mechanics are used to analyse this Gibbsian process. Furthermore, we prove spatially exponentially fast decreasing bounds for normalized local times of the edgereinforced random walk on a finite piece of the ladder, uniformly in the size of the finite piece. 1
Assessing the Order of Dependence for Partially Exchangeable Binary Data
, 1998
"... The problem we consider is how to assess the order of serial dependence within partially exchangeable binary sequences. We obtain exact conditional tests comparing any two orders by finding the conditional distribution of data given certain transition counts. These tests are facilitated with a new M ..."
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Cited by 6 (4 self)
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The problem we consider is how to assess the order of serial dependence within partially exchangeable binary sequences. We obtain exact conditional tests comparing any two orders by finding the conditional distribution of data given certain transition counts. These tests are facilitated with a new Monte Carlo scheme. Asymptotic tests are also discussed. In particular, we show that the likelihood ratio tests have an asymptotic Ø 2 distribution, thus generalizing the results of Billingsley (1961) for the particular case of Markov chains. We apply these methods to several data sets, and perform a simulation to study their properties. Keywords: conditional simulation, Markov chains, model selection, nonparametric mixtures, multiple binary sequences. 1 INTRODUCTION This paper is concerned with the nonparametric statistical analysis of multiple binary sequences, a commonly occurring data structure. One example we consider comes from dairy science, where each of a number of cows is tested...
Use of exchangeable pairs in the analysis of simulations
 Department of Statistics University of California Berkeley, CA 94720 Email: sourav@stat.berkeley.edu Department of Mathematics Hong Kong University of Science and Technology Clear Water Bay, Kowloon, Hong Kong China
, 2004
"... The method of exchangeable pairs has emerged as an important tool in proving limit theorems for Poisson, normal and other classical approximations. Here the method is used in a simulation context. We estimate transition probabilitites from the simulations and use these to reduce variances. Exchangea ..."
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Cited by 3 (0 self)
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The method of exchangeable pairs has emerged as an important tool in proving limit theorems for Poisson, normal and other classical approximations. Here the method is used in a simulation context. We estimate transition probabilitites from the simulations and use these to reduce variances. Exchangeable pairs are used as control variates. Finally, a general approximation theorem is developed that can be complemented by simulations to provide actual estimates of approximation errors. 1
Multiparticle processes with reinforcements, online
, 2005
"... The multiparticle generalization of the edgereinforced random walk is stated. Some recurrence results are obtained. 1 ..."
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Cited by 2 (1 self)
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The multiparticle generalization of the edgereinforced random walk is stated. Some recurrence results are obtained. 1