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52
Slice Sampling Mixture Models
"... We propose a more efficient version of the slice sampler for Dirichlet process mixture models described by Walker (2007). This sampler allows the fitting of infinite mixture models with a wide–range of prior specification. To illustrate this flexiblity we develop a new nonparametric prior for mixtur ..."
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Cited by 42 (2 self)
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We propose a more efficient version of the slice sampler for Dirichlet process mixture models described by Walker (2007). This sampler allows the fitting of infinite mixture models with a wide–range of prior specification. To illustrate this flexiblity we develop a new nonparametric prior for mixture models by normalizing an infinite sequence of independent positive random variables and show how the slice sampler can be applied to make inference in this model. Two submodels are studied in detail. The first one assumes that the positive random variables are Gamma distributed and the second assumes that they are inverse– Gaussian distributed. Both priors have two hyperparameters and we consider their effect on the prior distribution of the number of occupied clusters in a sample. Extensive computational comparisons with alternative ”conditional” simulation techniques for mixture models using the standard Dirichlet process prior and our new prior are made. The properties of the new prior are illustrated on a density estimation problem.
The Infinite Factorial Hidden Markov Model
"... We introduce a new probability distribution over a potentially infinite number of binary Markov chains which we call the Markov Indian buffet process. This process extends the IBP to allow temporal dependencies in the hidden variables. We use this stochastic process to build a nonparametric extensio ..."
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Cited by 35 (6 self)
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We introduce a new probability distribution over a potentially infinite number of binary Markov chains which we call the Markov Indian buffet process. This process extends the IBP to allow temporal dependencies in the hidden variables. We use this stochastic process to build a nonparametric extension of the factorial hidden Markov model. After constructing an inference scheme which combines slice sampling and dynamic programming we demonstrate how the infinite factorial hidden Markov model can be used for blind source separation. 1
The Infinite Partially Observable Markov Decision Process
"... The Partially Observable Markov Decision Process (POMDP) framework has proven useful in planning domains where agents must balance actions that provide knowledge and actions that provide reward. Unfortunately, most POMDPs are complex structures with a large number of parameters. In many realworld p ..."
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Cited by 25 (2 self)
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The Partially Observable Markov Decision Process (POMDP) framework has proven useful in planning domains where agents must balance actions that provide knowledge and actions that provide reward. Unfortunately, most POMDPs are complex structures with a large number of parameters. In many realworld problems, both the structure and the parameters are difficult to specify from domain knowledge alone. Recent work in Bayesian reinforcement learning has made headway in learning POMDP models; however, this work has largely focused on learning the parameters of the POMDP model. We define an infinite POMDP (iPOMDP) model that does not require knowledge of the size of the state space; instead, it assumes that the number of visited states will grow as the agent explores its world and only models visited states explicitly. We demonstrate the iPOMDP on several standard problems. 1
Bayesian Nonparametric Hidden SemiMarkov Models
 Journal of Machine Learning Research
"... There is much interest in the Hierarchical Dirichlet Process Hidden Markov Model (HDPHMM) as a natural Bayesian nonparametric extension of the ubiquitous Hidden Markov Model for learning from sequential and timeseries data. However, in many settings the HDPHMM’s strict Markovian constraints are u ..."
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Cited by 21 (3 self)
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There is much interest in the Hierarchical Dirichlet Process Hidden Markov Model (HDPHMM) as a natural Bayesian nonparametric extension of the ubiquitous Hidden Markov Model for learning from sequential and timeseries data. However, in many settings the HDPHMM’s strict Markovian constraints are undesirable, particularly if we wish to learn or encode nongeometric state durations. We can extend the HDPHMM to capture such structure by drawing upon explicitduration semiMarkov modeling, which has been developed mainly in the parametric nonBayesian setting, to allow construction of highly interpretable models that admit natural prior information on state durations. In this paper we introduce the explicitduration Hierarchical Dirichlet Process Hidden semiMarkov Model (HDPHSMM) and develop sampling algorithms for efficient posterior inference. The methods we introduce also provide new methods for sampling inference in the finite Bayesian HSMM. Our modular Gibbs sampling methods can be embedded in samplers for larger hierarchical Bayesian models, adding semiMarkov chain modeling as another tool in the Bayesian inference toolbox. We demonstrate the utility of the HDPHSMM and our inference methods on both synthetic and real experiments.
Dynamic Infinite Relational Model for Timevarying Relational Data Analysis
"... We propose a new probabilistic model for analyzing dynamic evolutions of relational data, such as additions, deletions and split & merge, of relation clusters like communities in social networks. Our proposed model abstracts observed timevarying objectobject relationships into relationships bet ..."
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Cited by 20 (2 self)
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We propose a new probabilistic model for analyzing dynamic evolutions of relational data, such as additions, deletions and split & merge, of relation clusters like communities in social networks. Our proposed model abstracts observed timevarying objectobject relationships into relationships between object clusters. We extend the infinite Hidden Markov model to follow dynamic and timesensitive changes in the structure of the relational data and to estimate a number of clusters simultaneously. We show the usefulness of the model through experiments with synthetic and realworld data sets. 1
The infinite HMM for unsupervised PoS tagging
 In Proceedings of 2009 Conference on Empirical Methods in Natural Language Processing
, 2009
"... We extend previous work on fully unsupervised partofspeech tagging. Using a nonparametric version of the HMM, called the infinite HMM (iHMM), we address the problem of choosing the number of hidden states in unsupervised Markov models for PoS tagging. We experiment with two nonparametric priors, ..."
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Cited by 16 (5 self)
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We extend previous work on fully unsupervised partofspeech tagging. Using a nonparametric version of the HMM, called the infinite HMM (iHMM), we address the problem of choosing the number of hidden states in unsupervised Markov models for PoS tagging. We experiment with two nonparametric priors, the Dirichlet and PitmanYor processes, on the Wall Street Journal dataset using a parallelized implementation of an iHMM inference algorithm. We evaluate the results with a variety of clustering evaluation metrics and achieve equivalent or better performances than previously reported. Building on this promising result we evaluate the output of the unsupervised PoS tagger as a direct replacement for the output of a fully supervised PoS tagger for the task of shallow parsing and compare the two evaluations. 1
Nonparametric Bayesian Policy Priors for Reinforcement Learning
 In Neural Information Processing Systems (NIPS
, 2010
"... We consider reinforcement learning in partially observable domains where the agent can query an expert for demonstrations. Our nonparametric Bayesian approach combines model knowledge, inferred from expert information and independent exploration, with policy knowledge inferred from expert trajectori ..."
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Cited by 12 (2 self)
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We consider reinforcement learning in partially observable domains where the agent can query an expert for demonstrations. Our nonparametric Bayesian approach combines model knowledge, inferred from expert information and independent exploration, with policy knowledge inferred from expert trajectories. We introduce priors that bias the agent towards models with both simple representations and simple policies, resulting in improved policy and model learning. 1
Inducing Synchronous Grammars with Slice Sampling
"... This paper describes an efficient sampler for synchronous grammar induction under a nonparametric Bayesian prior. Inspired by ideas from slice sampling, our sampler is able to draw samples from the posterior distributions of models for which the standard dynamic programing based sampler proves intra ..."
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Cited by 10 (0 self)
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This paper describes an efficient sampler for synchronous grammar induction under a nonparametric Bayesian prior. Inspired by ideas from slice sampling, our sampler is able to draw samples from the posterior distributions of models for which the standard dynamic programing based sampler proves intractable on nontrivial corpora. We compare our sampler to a previously proposed Gibbs sampler and demonstrate strong improvements in terms of both training loglikelihood and performance on an endtoend translation evaluation. 1
Sparse covariance estimation in heterogeneous samples
, 2011
"... Standard Gaussian graphical models implicitly assume that the conditional independence among variables is common to all observations in the sample. However, in practice, observations are usually collected from heterogeneous populations where such an assumption is not satisfied, leading in turn to no ..."
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Cited by 9 (2 self)
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Standard Gaussian graphical models implicitly assume that the conditional independence among variables is common to all observations in the sample. However, in practice, observations are usually collected from heterogeneous populations where such an assumption is not satisfied, leading in turn to nonlinear relationships among variables. To address such situations we explore mixtures of Gaussian graphical models; in particular, we consider both infinite mixtures and infinite hidden Markov models where the emission distributions correspond to Gaussian graphical models. Such models allow us to divide a heterogeneous population into homogenous groups, with each cluster having its own conditional independence structure. As an illustration, we study the trends in foreign exchange rate fluctuations in the preEuro era.
Detecting Abnormal Events via Hierarchical Dirichlet Processes
"... Abstract. Detecting abnormal event from video sequences is an important problem in computer vision and pattern recognition and a large number of algorithms have been devised to tackle this problem. Previous statebased approaches all suffer from the problem of deciding the appropriate number of stat ..."
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Cited by 9 (3 self)
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Abstract. Detecting abnormal event from video sequences is an important problem in computer vision and pattern recognition and a large number of algorithms have been devised to tackle this problem. Previous statebased approaches all suffer from the problem of deciding the appropriate number of states and it is often difficult to do so except using a trialanderror approach, which may be infeasible in realworld applications. Yet in this paper, we have proposed a more accurate and flexible algorithm for abnormal event detection from video sequences. Our threephase approach first builds a set of weak classifiers using Hierarchical Dirichlet Process Hidden Markov Model (HDPHMM), and then proposes an ensemble learning algorithm to filter out abnormal events. In the final phase, we will derive abnormal activity models from the normal activity model to reduce the FP (False Positive) rate in an unsupervised manner. The main advantage of our algorithm over previous ones is to naturally capture the underlying feature in abnormal event detection via HDPHMM. Experimental results on a realworld video sequence dataset have shown the effectiveness of our algorithm. 1