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. Key words and phrases: Probabilistic graphical models, junction tree algorithm, sum-product algorithm, Markov chain Monte Carlo, variational inference, bioinformatics, error-control coding.

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.

A fundamental problem in text data mining is to extract meaningful structure from document streams that arrive continuously over time. E-mail and news articles are two natural examples of such streams, each characterized by topics that appear, grow in intensity for a period of time, and then fade away. The published literature in a particular research field can be seen to exhibit similar phenomena over a much longer time scale. Underlying much of the text mining work in this area is the following intuitive premise --- that the appearance of a topic in a document stream is signaled by a "burst of activity," with certain features rising sharply in frequency as the topic emerges.

In sequence modeling, we often wish to represent complex interaction between labels, such as when performing multiple, cascaded labeling tasks on the same sequence, or when longrange dependencies exist. We present dynamic conditional random fields (DCRFs), a generalization of linear-chain conditional random fields (CRFs) in which each time slice contains a set of state variables and edges---a distributed state representation as in dynamic Bayesian networks (DBNs)---and parameters are tied across slices. Since exact

Abstract not found

We present a new general framework for online probabilistic plan recognition called the Abstract Hidden Markov Memory Model (AHMEM). The new model is an extension of the existing Abstract Hidden Markov Model to allow the policy to have internal memory which can be updated in a Markov fashion. We show that the AHMEM can represent a richer class of probabilistic plans, and at the same time derive an efficient algorithm for plan recognition in the AHMEM based on the RaoBlackwellised Particle Filter approximate inference method.

Structure elements in a time sequence (e.g. video) are repetitive segments with consistent deterministic or stochastic characteristics. While most existing work in detecting structures follow a supervised paradigm, we propose a fully unsupervised statistical solution in this paper. We present a unified approach to structure discovery from long video sequences as simultaneously finding the statistical descriptions of structure and locating segments that matches the descriptions. We model the multilevel statistical structure as hierarchical hidden Markov models, and present efficient algorithms for learning both the parameters and the model structure. When tested on a specific domain, soccer video, the unsupervised learning scheme achieves very promising results: it automatically discovers the statistical descriptions of high-level structures, and at the same time achieves even slightly better accuracy in detecting discovered structures in unlabelled videos than a supervised approach designed with domain knowledge and trained with comparable hidden Markov models.

Abstract not found

Dynamic Bayesian networks (DBNs) offer an elegant way to integrate various aspects of language in one model. Many existing algorithms developed for learning and inference in DBNs are applicable to probabilistic language modeling. To demonstrate the potential of DBNs for natural language processing, we employ a DBN in an information extraction task. We show how to assemble wealth of emerging linguistic instruments for shallow parsing, syntactic and semantic tagging, morphological decomposition, named entity recognition etc. in order to incrementally build a robust information extraction system. Our method outperforms previously published results on an established benchmark domain.

We explore the advantages of representing hierarchical partially observable Markov decision processes (H-POMDPs) as dynamic Bayesian networks (DBNs). In particular, we focus on the special case of using H-POMDPs to represent multiresolution spatial maps for indoor robot navigation. Our results show that a DBN representation of H-POMDPs can train significantly faster than the original learning algorithm for H-POMDPs or the equivalent flat POMDP, and requires much less data. In addition, the DBN formulation can easily be extended to parameter tying and factoring of variables, which further reduces the time and sample complexity. This enables us to apply H-POMDP methods to much larger problems than previously possible. 1.