Results 1 - 10
of
637
Hierarchical Dirichlet processes.
- Journal of the American Statistical Association,
, 2006
"... We consider problems involving groups of data where each observation within a group is a draw from a mixture model and where it is desirable to share mixture components between groups. We assume that the number of mixture components is unknown a priori and is to be inferred from the data. In this s ..."
Abstract
-
Cited by 942 (78 self)
- Add to MetaCart
(Show Context)
We consider problems involving groups of data where each observation within a group is a draw from a mixture model and where it is desirable to share mixture components between groups. We assume that the number of mixture components is unknown a priori and is to be inferred from the data. In this setting it is natural to consider sets of Dirichlet processes, one for each group, where the well-known clustering property of the Dirichlet process provides a nonparametric prior for the number of mixture components within each group. Given our desire to tie the mixture models in the various groups, we consider a hierarchical model, specifically one in which the base measure for the child Dirichlet processes is itself distributed according to a Dirichlet process. Such a base measure being discrete, the child Dirichlet processes necessarily share atoms. Thus, as desired, the mixture models in the different groups necessarily share mixture components. We discuss representations of hierarchical Dirichlet processes in terms of a stick-breaking process, and a generalization of the Chinese restaurant process that we refer to as the "Chinese restaurant franchise." We present Markov chain Monte Carlo algorithms for posterior inference in hierarchical Dirichlet process mixtures and describe applications to problems in information retrieval and text modeling.
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 ..."
Abstract
-
Cited by 806 (10 self)
- Add to MetaCart
(Show Context)
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 ..."
Abstract
-
Cited by 770 (3 self)
- Add to MetaCart
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.
Maximum entropy markov models for information extraction and segmentation
, 2000
"... Hidden Markov models (HMMs) are a powerful probabilistic tool for modeling sequential data, and have been applied with success to many text-related tasks, such as part-of-speech tagging, text segmentation and information extraction. In these cases, the observations are usually modeled as multinomial ..."
Abstract
-
Cited by 561 (18 self)
- Add to MetaCart
Hidden Markov models (HMMs) are a powerful probabilistic tool for modeling sequential data, and have been applied with success to many text-related tasks, such as part-of-speech tagging, text segmentation and information extraction. In these cases, the observations are usually modeled as multinomial distributions over a discrete vocabulary, and the HMM parameters are set to maximize the likelihood of the observations. This paper presents a new Markovian sequence model, closely related to HMMs, that allows observations to be represented as arbitrary overlapping features (such as word, capitalization, formatting, part-of-speech), and defines the conditional probability of state sequences given observation sequences. It does this by using the maximum entropy framework to fit a set of exponential models that represent the probability of a state given an observation and the previous state. We present positive experimental results on the segmentation of FAQ’s.
Coupled hidden Markov models for complex action recognition
, 1996
"... We present algorithms for coupling and training hidden Markov models (HMMs) to model interacting processes, and demonstrate their superiority to conventional HMMs in a vision task classifying two-handed actions. HMMs are perhaps the most successful framework in perceptual computing for modeling and ..."
Abstract
-
Cited by 501 (22 self)
- Add to MetaCart
We present algorithms for coupling and training hidden Markov models (HMMs) to model interacting processes, and demonstrate their superiority to conventional HMMs in a vision task classifying two-handed actions. HMMs are perhaps the most successful framework in perceptual computing for modeling and classifying dynamic behaviors, popular because they offer dynamic time warping, a training algorithm, and a clear Bayesian semantics. However, the Markovian framework makes strong restrictive assumptions about the system generating the signal---that it is a single process having a small number of states and an extremely limited state memory. The single-process model is often inappropriate for vision (and speech) applications, resulting in low ceilings on model performance. Coupled HMMs provide an efficient way to resolve many of these problems, and offer superior training speeds, model likelihoods, and robustness to initial conditions. 1. Introduction Computer vision is turning to problems...
A family of algorithms for approximate Bayesian inference
, 2001
"... One of the major obstacles to using Bayesian methods for pattern recognition has been its computational expense. This thesis presents an approximation technique that can perform Bayesian inference faster and more accurately than previously possible. This method, "Expectation Propagation," ..."
Abstract
-
Cited by 366 (11 self)
- Add to MetaCart
One of the major obstacles to using Bayesian methods for pattern recognition has been its computational expense. This thesis presents an approximation technique that can perform Bayesian inference faster and more accurately than previously possible. This method, "Expectation Propagation," unifies and generalizes two previous techniques: assumeddensity filtering, an extension of the Kalman filter, and loopy belief propagation, an extension of belief propagation in Bayesian networks. The unification shows how both of these algorithms can be viewed as approximating the true posterior distribution with a simpler distribution, which is close in the sense of KL-divergence. Expectation Propagation exploits the best of both algorithms: the generality of assumed-density filtering and the accuracy of loopy belief propagation. Loopy belief propagation, because it propagates exact belief states, is useful for limited types of belief networks, such as purely discrete networks. Expectation Propagati...
The Hierarchical Hidden Markov Model: Analysis and Applications
- MACHINE LEARNING
, 1998
"... . We introduce, analyze and demonstrate a recursive hierarchical generalization of the widely used hidden Markov models, which we name Hierarchical Hidden Markov Models (HHMM). Our model is motivated by the complex multi-scale structure which appears in many natural sequences, particularly in langua ..."
Abstract
-
Cited by 326 (3 self)
- Add to MetaCart
. We introduce, analyze and demonstrate a recursive hierarchical generalization of the widely used hidden Markov models, which we name Hierarchical Hidden Markov Models (HHMM). Our model is motivated by the complex multi-scale structure which appears in many natural sequences, particularly in language, handwriting and speech. We seek a systematic unsupervised approach to the modeling of such structures. By extendingthe standard forward-backward(BaumWelch) algorithm, we derive an efficient procedure for estimating the model parameters from unlabeled data. We then use the trained model for automatic hierarchical parsing of observation sequences. We describe two applications of our model and its parameter estimation procedure. In the first application we show how to construct hierarchical models of natural English text. In these models different levels of the hierarchy correspond to structures on different length scales in the text. In the second application we demonstrate how HHMMs can b...
Tractable inference for complex stochastic processes
- In Proc. UAI
, 1998
"... The monitoring and control of any dynamic system depends crucially on the ability to reason about its current status and its future trajectory. In the case of a stochastic system, these tasks typically involve the use of a belief state—a probability distribution over the state of the process at a gi ..."
Abstract
-
Cited by 302 (14 self)
- Add to MetaCart
(Show Context)
The monitoring and control of any dynamic system depends crucially on the ability to reason about its current status and its future trajectory. In the case of a stochastic system, these tasks typically involve the use of a belief state—a probability distribution over the state of the process at a given point in time. Unfortunately, the state spaces of complex processes are very large, making an explicit representation of a belief state intractable. Even in dynamic Bayesian networks (DBNs), where the process itself can be represented compactly, the representation of the belief state is intractable. We investigate the idea of maintaining a compact approximation to the true belief state, and analyze the conditions under which the errors due to the approximations taken over the lifetime of the process do not accumulate to make our answers completely irrelevant. We show that the error in a belief state contracts exponentially as the process evolves. Thus, even with multiple approximations, the error in our process remains bounded indefinitely. We show how the additional structure of a DBN can be used to design our approximation scheme, improving its performance significantly. We demonstrate the applicability of our ideas in the context of a monitoring task, showing that orders of magnitude faster inference can be achieved with only a small degradation in accuracy. 1
Hierarchical topic models and the nested Chinese restaurant process
- Advances in Neural Information Processing Systems
, 2004
"... We address the problem of learning topic hierarchies from data. The model selection problem in this domain is daunting—which of the large collection of possible trees to use? We take a Bayesian approach, generating an appropriate prior via a distribution on partitions that we refer to as the nested ..."
Abstract
-
Cited by 287 (32 self)
- Add to MetaCart
(Show Context)
We address the problem of learning topic hierarchies from data. The model selection problem in this domain is daunting—which of the large collection of possible trees to use? We take a Bayesian approach, generating an appropriate prior via a distribution on partitions that we refer to as the nested Chinese restaurant process. This nonparametric prior allows arbitrarily large branching factors and readily accommodates growing data collections. We build a hierarchical topic model by combining this prior with a likelihood that is based on a hierarchical variant of latent Dirichlet allocation. We illustrate our approach on simulated data and with an application to the modeling of NIPS abstracts. 1
