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.

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 self-adjoint operator with criteria for an eigenvector to descend to an orbit graph. As examples, we show that the Metropolis construction can dominate a max-degree construction by an arbitrary amount and that, in turn, the fastest mixing Markov chain can dominate the Metropolis construction by an arbitrary amount. 1

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...

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 so-called 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.

We prove that the edge-reinforced random walk on the ladder Z × {1,2} with initial weights a> 3/4 is recurrent. The proof uses a known representation of the edge-reinforced 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 edge-reinforced random walk on a finite piece of the ladder, uniformly in the size of the finite piece. 1

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...

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 life-like computer game characters. Following our general strategy of analyzing the network traffic of multi-player 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 human-like.

The multi-particle generalization of the edge-reinforced random walk is stated. Some recurrence results are obtained. 1

We show that a large collection of statistical mechanical systems with quadratically represented Hamiltonians on the complete graph can be extended to infinite exchangeable processes. This extends a known result for the ferromagnetic Curie–Weiss Ising model and includes as well all ferromagnetic Curie–Weiss Potts and Curie–Weiss Heisenberg models. By de Finetti’s theorem, this is equivalent to showing that these probability measures can be expressed as averages of product measures. We provide examples showing that “ferromagnetism” is not however in itself sufficient and also study in some detail the Curie–Weiss Ising model with an additional 3-body interaction. Finally, we study the question of how much the antiferromagnetic Curie–Weiss Ising model can be extended. In this direction, we obtain sharp asymptotic results via a solution to a new moment problem. We also obtain a “formula ” for the extension which is valid in many cases.

This paper presents a Bayesian nonparametric approach to survival analysis based on arbitrarly right censored data. The first aim will be to show that the neutral to the right process is the natural prior to use in this context. Secondly, the properties of a particular neutral to the right process, the beta-Stacy process are examined. Finally, the connections between some Bayesian bootstraps and the beta-Stacy process are investigated. KEY WORDS: Bayesian bootstrap, Censoring, Exchangeability, Neutral to the right process, Predicition AMS 1991 Subject classifications: Primary 62A15 - Secondary 62M20. -- v -- Contents 1 Introduction 1 2 Preliminaries 2 3 A predictive approach 3 4 The beta-Stacy process 6 5 Exchangeable neutral urn scheme 10 6 Bayesian bootstraps 11 References -- 1 -- Neutral to the Right Processes from a Predictive Perspective: A Review and New Developments Pietro Muliere Stephen Walker 1 Introduction This paper deals with survival analysis from incomplete observ...