Phylogenetics is the study of the evolutionary relationship between species. Inference of phylogeny relies heavily on statistical models that have been extended and refined tremendously over the past years into very complex hierarchical models. Paper I introduces probabilistic graphical models to statistical phylogenetics and elaborates on the potential advantages a unified graphical model representation could have for the community, e.g., by facilitating communication and improving reproducibility of statistical analyses of phylogeny and evolution. Once the phylogeny is reconstructed it is possible to infer the rates of diversification (speciation and extinction). In this thesis I extend the birth-death process model, so that it can be applied to incompletely sampled phylogenies, that is, phylogenies of only a subsample of the presently living species from one group. Previous work only considered the case when every species had the same probability to be included and here I examine two alternative sampling schemes: diversified taxon sampling and cluster sampling. Paper II introduces these sampling schemes under a constant rate birth-death process and gives the probability density for reconstructed phylogenies. These models are extended in Paper IV to time-dependent diversification rates, again, under different sampling schemes and applied to empirical phylogenies. Paper III focuses on fast and unbiased simulations of reconstructed phylogenies. The efficiency is achieved by deriving the analytical distribution and density function of the speciation times in the reconstructed phylogeny. / <p>At the time of the doctoral defense, the following papers were unpublished and had a status as follows: Paper 1: Manuscript. Paper 4: Accepted.</p>

This thesis introduces principled, broadly applicable, and efficient patch-based models for data processing applications. Recently, "epitomes" were introduced as patch-based probability models that are learned by compiling together a large number of examples of patches from input images. This thesis describes how epitomes can be used to model video data and a significant computational speedup is introduced that can be incorporated into the epitome inference and learning algorithm. In the case of videos, epitomes are estimated so as to model most of the small space-time cubes from the input data. Then, the epitome can be used for various modelling and reconstruction tasks, of which we show results for video super-resolution, video interpolation, and object removal. Besides computational efficiency, an interesting advantage of the epitome as a representation is that it can be reliably estimated even from videos with large amounts of missing data. This ability is illustrated on the task of reconstructing the dropped frames in a video broadcast using only the degraded video. Further, a new patch-based model is introduced, that when applied to epitomes, accounts for the varying geometric configurations of object features. The power of this model is illustrated on tasks such as multiple object registration and detection and missing data interpolation, including a difficult task of photograph relighting.

Alternative splicing, the process by which a single gene may code for similar but different proteins, is an important process in biology, linked to development, cellular differentiation, genetic diseases, and more. Genome-wide analysis of alternative splicing patterns and regulation has been recently made possible due to new high throughput techniques for monitoring gene expression and genomic sequencing. This thesis introduces two algorithms for alternative splicing analysis based on large microarray and genomic sequence data. The algorithms, based on generative probabilistic models that capture structure and patterns in the data, are used to study global properties of alternative splicing. In the first part of the thesis, a microarray platform for monitoring alternative splicing is introduced. A spatial noise removal algorithm that removes artifacts and improves data fidelity is presented. The GenASAP algorithm (generative model for alternative splicing array platform) models the non-linear process in which targeted molecules bind to a microarray’s probes and is used to predict patterns of alternative splicing. Two versions of GenASAP have been developed. The first uses variational approximation to infer the relative amounts of the targeted molecules, while the second incorporates a more accurate noise and generative model and utilizes Markov chain Monte Carlo (MCMC) sampling. GenASAP, the first method to provide quantitative predictions of alternative splicing patterns on large scale data sets, is shown to generate useful and precise predictions based on independent RT-PCR validation (a slow but more accurate approach to measuring cellular expression patterns). In the second part of the thesis, the results obtained by GenASAP are analysed to reveal jointly regulated genes. The sequences of the genes are examined for potential regulatory factors binding sites using a new motif finding algorithm designed for this purpose. The motif finding algorithm, called GenBITES (generative model for binding sites) uses a fully Bayesian generative model for sequences, and the MCMC approach used for inference in the model includes moves that can efficiently create or delete motifs, and extend or contract the width of existing motifs. GenBITES has been applied to several synthetic and real data sets, and is shown to be highly competitive at a task for which many algorithms already exist. Although developed to analyze alternative splicing data, GenBITES outperforms most reported results on a benchmark data set based on transcription data.

Discrete location analysis is one of the most widely studied branches of operations research, whose applications arise in a wide variety of settings. This thesis describes a powerful new approach to facility location problems - that of message passing inference in probabilistic graphical models. Using this framework, we develop new heuristic algorithms, as well as a new approximation algorithm for a particular problem type. In machine learning applications, facility location can be seen a discrete formulation of clustering and mixture modeling problems. We apply the developed algorithms to such problems in computer vision. We tackle the problem of motion segmentation in video sequences by formulating it as a facility location instance and demonstrate the advantages of message passing algorithms over current segmentation methods.

This thesis introduces principled, broadly applicable, and efficient patch-based models for data processing applications. Recently, "epitomes" were introduced as patch-based probability models that are learned by compiling together a large number of examples of patches from input images. This thesis describes how epitomes can be used to model video data and a significant computational speedup is introduced that can be incorporated into the epitome inference and learning algorithm. In the case of videos, epitomes are estimated so as to model most of the small space-time cubes from the input data. Then, the epitome can be used for various modelling and reconstruction tasks, of which we show results for video super-resolution, video interpolation, and object removal. Besides computational efficiency, an interesting advantage of the epitome as a representation is that it can be reliably estimated even from videos with large amounts of missing data. This ability is illustrated on the task of reconstructing the dropped frames in a video broadcast using only the degraded video. Further, a new patch-based model is introduced, that when applied to epitomes, accounts for the varying geometric configurations of object features. The power of this model is illustrated on tasks such as multiple object registration and detection and missing data interpolation, including a difficult task of photograph relighting.

Given that phishing is an ever increasing problem, a better authentication system than the current alphanumeric system is needed. Because of the large number of current authentication systems that use alphanumeric passwords, a new solution should be compatible with these systems. We propose a system that uses a graphical password deployed from a Trojan and virus resistant embedded device as a possible solution. The graphical password would require the user to choose a family photo sized to 441x331 pixels. Using this image, a novel, image hash provides an input into a cryptosystem on the embedded device that subsequently returns an encryption key or text password. The graphical password requires the user to click five to eight points on the image. From these click-points, the embedded device stretches the graphical password input to a 32- character, random, unique alphanumeric password or a 256-bit AES key. Each embedded device and image are unique components in the graphical password system. Additionally, one graphical password can generate many 32-character unique, alphanumeric passwords using its embedded device which eliminates the need for the user to memorize many passwords. / Computer Engineering

This thesis deals with the use of Conditional Random Fields (CRFs; Lafferty et al. (2001)) for Natural Language Processing (NLP). CRFs are probabilistic models for sequence labelling which are particularly well suited to NLP. They have many compelling advantages over other popular models such as Hidden Markov Models and Maximum Entropy Markov Models (Rabiner, 1990; McCallum et al., 2001), and have been applied to a number of NLP tasks with considerable success (e.g., Sha and Pereira (2003) and Smith et al. (2005)). Despite their apparent success, CRFs suffer from two main failings. Firstly, they often over-fit the training sample. This is a consequence of their considerable expressive power, and can be limited by a prior over the model parameters (Sha and Pereira, 2003; Peng and McCallum, 2004). Their second failing is that the standard methods for CRF training are often very slow, sometimes requiring weeks of processing time. This efficiency problem is largely ignored in current literature, although in practise the cost of training prevents the application of CRFs to many new more complex tasks, and also prevents the use of densely connected graphs, which would allow for much richer feature sets. (For complete abstract open document)

Thesis (DDes) - Faculty of Design, Swinburne University of Technology, 2006. / Submitted in partial fulfilment of the requirements of the degree of Professional Doctorate in Design, Faculty of Design, Swinburne University of Technology - 2006. Typescript. Bibliography: p. 76-85.

Thesis (M.App.Sc.) - Carleton University, 2005. / Includes bibliographical references (p. 108-112). Also available in electronic format on the Internet.

Report (M.S.)--Virginia Polytechnic Institute and State University, 1994. / Abstract. Includes bibliographical references (leaves 88-91). Also available via the Internet.