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.

Several authors in recent years have proposed discrete analogues to principle component analysis intended to handle discrete or positive only data, for instance suited to analyzing sets of documents. Methods include non-negative matrix factorization, probabilistic latent semantic analysis, and latent Dirichlet allocation. This paper begins with a review of the basic theory of the variational extension to the expectation maximization algorithm, and then presents discrete component finding algorithms in that light. Experiments are conducted on both bigram word data and document bag-of-word to expose some of the subtleties of this new class of algorithms.

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The mutual information of two random variables i and j with joint probabilities t ij is commonly used in learning Bayesian nets as well as in many other fields. The chances t ij are usually estimated by the empirical sampling frequency n ij /n leading to a point estimate I(n ij /n) for the mutual information. To answer questions like "is I(n ij /n) consistent with zero?" or "what is the probability that the true mutual information is much larger than the point estimate?" one has to go beyond the point estimate. In the Bayesian framework one can answer these questions by utilizing a (second order) prior distribution p(t) comprising prior information about t. From the prior p(t) one can compute the posterior p(t|n), from which the distribution p(I|n) of the mutual information can be calculated. We derive reliable and quickly computable approximations for p(I|n). We concentrate on the mean, variance, skewness, and kurtosis, and non-informative priors. For the mean we also give an exact expression. Numerical issues and the range of validity are discussed.

We propose a new unsupervised training method for acquiring...

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.

In this paper, we present algorithms for unsupervised mining of structures in video using multiscale statistical models. Video structure are repetitive segments in a video stream with consistent statistical characteristics. Such structures can often be interpreted in relation to distinctive semantics, particularly in structured domains like sports. While much work in the literature explores the link between the observations and the semantics using supervised learning, we propose unsupervised structure mining algorithms that aim at alleviating the burden of labelling and training, as well as providing a scalable solution for generalizing video indexing techniques to heterogeneous content collections such as surveillance and consumer videos. Existing unsupervised video structuring works primarily use clustering techniques, while the rich statistical characteristics in the temporal dimension at different granularity remain unexplored. Automatically identifying structures from an unknown domain poses significant challenges when domain knowledge is not explicitly present to assist algorithm design, model selection, and feature selection. In this work, we model multi-level statistical structures with hierarchical hidden Markov models based on a multi-level Markov dependency assumption. The parameters of the model are efficiently estimated using the EM algorithm, we have also developed a model structure learning algorithm that uses stochastic sampling techniques to find the optimal model structure, and a feature selection algorithm that automatically finds compact relevant feature sets using hybrid wrapper-filter methods. When tested on sports videos, the unsupervised learning scheme achieves very promising results: (1) The automatically selectead feature set...

We describe a new method for fitting mixture models to multivariate data which performs component selection and does not require external initialization. The novelty of our approach includes: an MML-like (minimum message length) model selection criterion; inclusion of the criterion into the expectation-maximization (EM) algorithm (increasing its ability to escape from local maxima); an initialization strategy supported on the interpretation of EM as a selfannealing algorithm. 1.

Statistical supervised learning techniques have been successful for many natural language processing tasks, but they require labeled datasets, which can be expensive to obtain. On the other hand, unlabeled data (raw text) is often available “for free ” in large quantities. Unlabeled data has shown promise in improving the performance of a number of tasks, e.g. word sense disambiguation, information extraction, and natural language parsing. In this thesis, we focus on two segmentation tasks, named-entity recognition and Chinese word segmentation. The goal of named-entity recognition is to detect and classify names of people, organizations, and locations in a sentence. The goal of Chinese word segmentation is to find the word boundaries in a sentence that has been written as a string of characters without spaces. Our approach is as follows: In a preprocessing step, we use raw text to cluster words and calculate mutual information statistics. The output of this step is then used as features in a supervised model, specifically a global linear model trained using

In this paper we describe a technique that allows the extraction of multiple local shift-invariant features from analysis of non-negative data of arbitrary dimensionality. Our approach employs a probabilistic latent variable model with sparsity constraints. We demonstrate its utility by performing feature extraction in a variety of domains ranging from audio to images and video. Index Terms — Feature extraction, Unsupervised learning 1.