Dirichlet process mixture models for unsupervised clustering of symptoms in Parkinson's disease

In this paper, the goal of identifying disease subgroups based on differences in observed symptom profile is considered. Commonly referred to as phenotype identification, solutions to this task often involve the application of unsupervised clustering techniques. In this paper, we investigate the application of a Dirichlet Process mixture (DPM) model for this task. This model is defined by the placement of the Dirichlet Process (DP) on the unknown components of a mixture model, allowing for the expression of uncertainty about the partitioning of observed data into homogeneous subgroups. To exemplify this approach, an application to phenotype identification in Parkinson’s disease (PD) is considered, with symptom profiles collected using the Unified Parkinson’s Disease Rating Scale (UPDRS). Clustering, Dirichlet Process mixture, Parkinson’s disease, UPDRS.

Fast re-parameterisation of Gaussian mixture models for robotics applications

Autonomous navigation and picture compilation tasks require robust feature descriptions or models. Given the non Gaussian nature of sensor observations, it will be shown that Gaussian mixture models provide a general probabilistic representation allowing analytical solutions to the update and prediction operations in the general Bayesian filtering problem. Each operation in the Bayesian filter for Gaussian mixture models multiplicatively increases the number of parameters in the representation leading to the need for a re-parameterisation step. A computationally efficient re-parameterisation step will be demonstrated resulting in a compact and accurate estimate of the true distribution.

Using Bayesian Mixture Models That Combine Expert Knowledge and GIS Data to Define Ecoregions

Conservation planning and management programs typically assume relatively homogeneous ecological landscapes. Such “ecoregions” serve multiple purposes: they support assessments of competing environmental values, reveal priorities for allocating scarce resources, and guide effective on-ground actions such as the acquisition of a protected area and habitat restoration. Ecoregions have evolved from a history of organism–environment interactions, and are delineated at the scale or level of detail required to support planning. Depending on the delineation method, scale, or purpose, they have been described as provinces, zones, systems, land units, classes, facets, domains, subregions, and ecological, biological, biogeographical, or environmental regions. In each case, they are essential to the development of conservation strategies and are embedded in government policies at multiple scales.

Mixture models of nucleotide sequence evolution that account for heterogeneity in the substitution process across sites and across lineages

Molecular phylogenetic studies of homologous sequences of nucleotides often assume that the underlying evolutionary process was globally stationary, reversible, and homogeneous (SRH), and that a model of evolution with one or more site-specific and time-reversible rate matrices (e.g., the GTR rate matrix) is enough to accurately model the evolution of data over the whole tree. However, an increasing body of data suggests that evolution under these conditions is an exception, rather than the norm. To address this issue, several non-SRH models of molecular evolution have been proposed, but they either ignore heterogeneity in the substitution process across sites (HAS) or assume it can be modeled accurately using the distribution. As an alternative to these models of evolution, we introduce a family of mixture models that approximate HAS without the assumption of an underlying predefined statistical distribution. This family of mixture models is combined with non-SRH models of evolution that account for heterogeneity in the substitution process across lineages (HAL). We also present two algorithms for searching model space and identifying an optimal model of evolution that is less likely to over- or underparameterize the data. The performance of the two new algorithms was evaluated using alignments of nucleotides with 10 000 sites simulated under complex non-SRH conditions on a 25-tipped tree. The algorithms were found to be very successful, identifying the correct HAL model with a 75% success rate (the average success rate for assigning rate matrices to the tree's 48 edges was 99.25%) and, for the correct HAL model, identifying the correct HAS model with a 98% success rate. Finally, parameter estimates obtained under the correct HAL-HAS model were found to be accurate and precise. The merits of our new algorithms were illustrated with an analysis of 42 337 second codon sites extracted from a concatenation of 106 alignments of orthologous genes encoded by the nuclear genomes of Saccharomyces cerevisiae, S. paradoxus, S. mikatae, S. kudriavzevii, S. castellii, S. kluyveri, S. bayanus, and Candida albicans. Our results show that second codon sites in the ancestral genome of these species contained 49.1% invariable sites, 39.6% variable sites belonging to one rate category (V1), and 11.3% variable sites belonging to a second rate category (V2). The ancestral nucleotide content was found to differ markedly across these three sets of sites, and the evolutionary processes operating at the variable sites were found to be non-SRH and best modeled by a combination of eight edge-specific rate matrices (four for V1 and four for V2). The number of substitutions per site at the variable sites also differed markedly, with sites belonging to V1 evolving slower than those belonging to V2 along the lineages separating the seven species of Saccharomyces. Finally, sites belonging to V1 appeared to have ceased evolving along the lineages separating S. cerevisiae, S. paradoxus, S. mikatae, S. kudriavzevii, and S. bayanus, implying that they might have become so selectively constrained that they could be considered invariable sites in these species.

Overfitting Bayesian mixture models with an unknown number of components

This paper proposes solutions to three issues pertaining to the estimation of finite mixture models with an unknown number of components: the non-identifiability induced by overfitting the number of components, the mixing limitations of standard Markov Chain Monte Carlo (MCMC) sampling techniques, and the related label switching problem. An overfitting approach is used to estimate the number of components in a finite mixture model via a Zmix algorithm. Zmix provides a bridge between multidimensional samplers and test based estimation methods, whereby priors are chosen to encourage extra groups to have weights approaching zero. MCMC sampling is made possible by the implementation of prior parallel tempering, an extension of parallel tempering. Zmix can accurately estimate the number of components, posterior parameter estimates and allocation probabilities given a sufficiently large sample size. The results will reflect uncertainty in the final model and will report the range of possible candidate models and their respective estimated probabilities from a single run. Label switching is resolved with a computationally light-weight method, Zswitch, developed for overfitted mixtures by exploiting the intuitiveness of allocation-based relabelling algorithms and the precision of label-invariant loss functions. Four simulation studies are included to illustrate Zmix and Zswitch, as well as three case studies from the literature. All methods are available as part of the R package Zmix, which can currently be applied to univariate Gaussian mixture models.

Incorporating uncertainty in environmental models informed by imagery

In this thesis, the issue of incorporating uncertainty for environmental modelling informed by imagery is explored by considering uncertainty in deterministic modelling, measurement uncertainty and uncertainty in image composition. Incorporating uncertainty in deterministic modelling is extended for use with imagery using the Bayesian melding approach. In the application presented, slope steepness is shown to be the main contributor to total uncertainty in the Revised Universal Soil Loss Equation. A spatial sampling procedure is also proposed to assist in implementing Bayesian melding given the increased data size with models informed by imagery. Measurement error models are another approach to incorporating uncertainty when data is informed by imagery. These models for measurement uncertainty, considered in a Bayesian conditional independence framework, are applied to ecological data generated from imagery. The models are shown to be appropriate and useful in certain situations. Measurement uncertainty is also considered in the context of change detection when two images are not co-registered. An approach for detecting change in two successive images is proposed that is not affected by registration. The procedure uses the Kolmogorov-Smirnov test on homogeneous segments of an image to detect change, with the homogeneous segments determined using a Bayesian mixture model of pixel values. Using the mixture model to segment an image also allows for uncertainty in the composition of an image. This thesis concludes by comparing several different Bayesian image segmentation approaches that allow for uncertainty regarding the allocation of pixels to different ground components. Each segmentation approach is applied to a data set of chlorophyll values and shown to have different benefits and drawbacks depending on the aims of the analysis.

Cross likelihood ratio based speaker clustering using eigenvoice models

This paper proposes the use of eigenvoice modeling techniques with the Cross Likelihood Ratio (CLR) as a criterion for speaker clustering within a speaker diarization system. The CLR has previously been shown to be a robust decision criterion for speaker clustering using Gaussian Mixture Models. Recently, eigenvoice modeling techniques have become increasingly popular, due to its ability to adequately represent a speaker based on sparse training data, as well as an improved capture of differences in speaker characteristics. This paper hence proposes that it would be beneficial to capitalize on the advantages of eigenvoice modeling in a CLR framework. Results obtained on the 2002 Rich Transcription (RT-02) Evaluation dataset show an improved clustering performance, resulting in a 35.1% relative improvement in the overall Diarization Error Rate (DER) compared to the baseline system.

Speaker identification using higher order spectral phase features and their effectiveness vis-a-vis Mel-Cepstral features

The effectiveness of higher-order spectral (HOS) phase features in speaker recognition is investigated by comparison with Mel Cepstral features on the same speech data. HOS phase features retain phase information from the Fourier spectrum unlikeMel–frequency Cepstral coefficients (MFCC). Gaussian mixture models are constructed from Mel– Cepstral features and HOS features, respectively, for the same data from various speakers in the Switchboard telephone Speech Corpus. Feature clusters, model parameters and classification performance are analyzed. HOS phase features on their own provide a correct identification rate of about 97% on the chosen subset of the corpus. This is the same level of accuracy as provided by MFCCs. Cluster plots and model parameters are compared to show that HOS phase features can provide complementary information to better discriminate between speakers.

Improved GMM-based speaker verification using SVM-driven impostor dataset selection

The problem of impostor dataset selection for GMM-based speaker verification is addressed through the recently proposed data-driven background dataset refinement technique. The SVM-based refinement technique selects from a candidate impostor dataset those examples that are most frequently selected as support vectors when training a set of SVMs on a development corpus. This study demonstrates the versatility of dataset refinement in the task of selecting suitable impostor datasets for use in GMM-based speaker verification. The use of refined Z- and T-norm datasets provided performance gains of 15% in EER in the NIST 2006 SRE over the use of heuristically selected datasets. The refined datasets were shown to generalise well to the unseen data of the NIST 2008 SRE.