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Murphy, Thomas Brendan
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Murphy, Thomas Brendan
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Murphy, Thomas Brendan
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Now showing 1 - 10 of 35
- PublicationJoint Modelling of Multiple Network ViewsLatent space models (LSM) for network data were introduced by Holf et al. (2002) under the basic assumption that each node of the network has an unknown position in a D-dimensional Euclidean latent space: generally the smaller the distance between two nodes in the latent space, the greater their probability of being connected. In this paper we propose a variational inference approach to estimate the intractable posterior of the LSM. In many cases, different network views on the same set of nodes are available. It can therefore be useful to build a model able to jointly summarise the information given by all the network views. For this purpose, we introduce the latent space joint model (LSJM) that merges the information given by multiple network views assuming that the probability of a node being connected with other nodes in each network view is explained by a unique latent variable. This model is demonstrated on the analysis of two datasets: an excerpt of 50 girls from 'Teenage Friends and Lifestyle Study' data at three time points and the Saccharomyces cerevisiae genetic and physical protein-protein interactions.
332 - PublicationVariable selection and updating in model-based discriminant analysis for high dimensional data with food authenticity applications(Institute of Mathematical Statistics, 2010-03)
; ; Food authenticity studies are concerned with determining if food samples have been correctly labelled or not. Discriminant analysis methods are an integral part of the methodology for food authentication. Motivated by food authenticity applications, a model-based discriminant analysis method that includes variable selection is presented. The discriminant analysis model is fitted in a semi-supervised manner using both labeled and unlabeled data. The method is shown to give excellent classification performance on several high-dimensional multiclass food authenticity datasets with more variables than observations. The variables selected by the proposed method provide information about which variables are meaningful for classification purposes. A headlong search strategy for variable selection is shown to be efficient in terms of computation and achieves excellent classification performance. In applications to several food authenticity datasets, our proposed method outperformed default implementations of Random Forests, AdaBoost, transductive SVMs and Bayesian Multinomial Regression by substantial margins.398Scopus© Citations 33 - PublicationA grade of membership model for rank data(International Society for Bayesian Analysis (ISBA), 2009-06)
; A grade of membership (GoM) model is an individual level mixture model which allows individuals have partial membership of the groups that characterize a population. A GoM model for rank data is developed to model the particular case when the response data is ranked in nature. A Metropolis-withinGibbs sampler provides the framework for model fitting, but the intricate nature of the rank data models makes the selection of suitable proposal distributions difficult. 'Surrogate' proposal distributions are constructed using ideas from optimization transfer algorithms. Model fitting issues such as label switching and model selection are also addressed. The GoM model for rank data is illustrated through an analysis of Irish election data where voters rank some or all of the candidates in order of preference. Interest lies in highlighting distinct groups of voters with similar preferences (i.e. 'voting blocs') within the electorate, taking into account the rank nature of the response data, and in examining individuals’ voting bloc memberships. The GoM model for rank data is fitted to data from an opinion poll conducted during the Irish presidential election campaign in 1997.278Scopus© Citations 33 - PublicationA mixture of experts model for rank data with applications in election studiesA voting bloc is defined to be a group of voters who have similar voting preferences. The cleavage of the Irish electorate into voting blocs is of interest. Irish elections employ a 'single transferable vote' electoral system; under this system voters rank some or all of the electoral candidates in order of preference. These rank votes provide a rich source of preference information from which inferences about the composition of the electorate may be drawn. Additionally, the influence of social factors or covariates on the electorate composition is of interest. A mixture of experts model is a mixture model in which the model parameters are functions of covariates. A mixture of experts model for rank data is developed to provide a model-based method to cluster Irish voters into voting blocs, to examine the influence of social factors on this clustering and to examine the characteristic preferences of the voting blocs. The Benter model for rank data is employed as the family of component densities within the mixture of experts model; generalized linear model theory is employed to model the influence of covariates on the mixing proportions. Model fitting is achieved via a hybrid of the EM and MM algorithms. An example of the methodology is illustrated by examining an Irish presidential election. The existence of voting blocs in the electorate is established and it is determined that age and government satisfaction levels are important factors in influencing voting in this election.
285Scopus© Citations 79 - PublicationAnalysis of Irish third-level college applications dataThe Irish college admissions system involves prospective students listing up to 10 courses in order of preference on their application. Places in third-level educational institutions are subsequently offered to the applicants on the basis of both their preferences and their final second-level examination results. The college applications system is a large area of public debate in Ireland. Detractors suggest that the process creates artificial demand for 'high profile' courses, causing applicants to ignore their vocational callings. Supporters argue that the system is impartial and transparent. The Irish college degree applications data from the year 2000 are analysed by using mixture models based on ranked data models to investigate the types of application behaviour that are exhibited by college applicants. The results of this analysis show that applicants form groups according to both the discipline and the geographical location of their course choices. In addition, there is evidence of the suggested 'points race' for high profile courses. Finally, gender emerges as an influential factor when studying course choice behaviour.
470Scopus© Citations 47 - PublicationModel-Based clustering of microarray expression data via latent Gaussian mixture modelsIn recent years, work has been carried out on clustering gene expression microarray data. Some approaches are developed from an algorithmic viewpoint whereas others are developed via the application of mixture models. In this article, a family of eight mixture models which utilizes the factor analysis covariance structure is extended to 12 models and applied to gene expression microarray data. This modelling approach builds on previous work by introducing a modified factor analysis covariance structure, leading to a family of 12 mixture models, including parsimonious models. This family of models allows for the modelling of the correlation between gene expression levels even when the number of samples is small. Parameter estimation is carried out using a variant of the expectation–maximization algorithm and model selection is achieved using the Bayesian information criterion. This expanded family of Gaussian mixture models, known as the expanded parsimonious Gaussian mixture model (EPGMM) family, is then applied to two well-known gene expression data sets.
378Scopus© Citations 108 - PublicationMultiresolution network models(Taylor & Francis, 2018-11-05)
; ; ; ; Many existing statistical and machine learning tools for social network analysis focus on a single level of analysis. Methods designed for clustering optimize a global partition of the graph, whereas projection-based approaches (e.g., the latent space model in the statistics literature) represent in rich detail the roles of individuals. Many pertinent questions in sociology and economics, however, span multiple scales of analysis. Further, many questions involve comparisons across disconnected graphs that will, inevitably be of different sizes, either due to missing data or the inherent heterogeneity in real-world networks. We propose a class of network models that represent network structure on multiple scales and facilitate comparison across graphs with different numbers of individuals. These models differentially invest modeling effort within subgraphs of high density, often termed communities, while maintaining a parsimonious structure between said subgraphs. We show that our model class is projective, highlighting an ongoing discussion in the social network modeling literature on the dependence of inference paradigms on the size of the observed graph. We illustrate the utility of our method using data on household relations from Karnataka, India. Supplementary material for this article is available online.443Scopus© Citations 9 - PublicationBayesian Nonparametric Plackett-Luce Models for the Analysis of Preferences for College Degree Programmes(Institute of Mathematical Statistics, 2014)
; ; In this paper we propose a Bayesian nonparametric model for clustering partial ranking data.We start by developing a Bayesian nonparametric extension of the popular Plackett-Luce choice model that can handle an infinite number of choice items. Our framework is based on the theory of random atomic measures, with prior specified by a completely random measure. We characterise the posterior distribution given data, and derive a simple and effective Gibbs sampler for posterior simulation. We then develop a Dirichlet process mixture extension of our model and apply it to investigate the clustering of preferences for college degree programmes amongst Irish secondary school graduates. The existence of clusters of applicants who have similar preferences for degree programmes is established and we determine that subject matter and geographical location of the third level institution characterise these clusters.261Scopus© Citations 32 - PublicationExponential family mixed membership models for soft clustering of multivariate dataFor several years, model-based clustering methods have successfully tackled many of the challenges presented by data-analysts. However, as the scope of data analysis has evolved, some problems may be beyond the standard mixture model framework. One such problem is when observations in a dataset come from overlapping clusters, whereby different clusters will possess similar parameters for multiple variables. In this setting, mixed membership models, a soft clustering approach whereby observations are not restricted to single cluster membership, have proved to be an effective tool. In this paper, a method for fitting mixed membership models to data generated by a member of an exponential family is outlined. The method is applied to count data obtained from an ultra running competition, and compared with a standard mixture model approach.
204Scopus© Citations 2 - PublicationModel-based clustering with sparse covariance matricesFinite Gaussian mixture models are widely used for model-based clustering of continuous data. Nevertheless, since the number of model parameters scales quadratically with the number of variables, these models can be easily over-parameterized. For this reason, parsimonious models have been developed via covariance matrix decompositions or assuming local independence. However, these remedies do not allow for direct estimation of sparse covariance matrices nor do they take into account that the structure of association among the variables can vary from one cluster to the other. To this end, we introduce mixtures of Gaussian covariance graph models for model-based clustering with sparse covariance matrices. A penalized likelihood approach is employed for estimation and a general penalty term on the graph configurations can be used to induce different levels of sparsity and incorporate prior knowledge. Model estimation is carried out using a structural-EM algorithm for parameters and graph structure estimation, where two alternative strategies based on a genetic algorithm and an efficient stepwise search are proposed for inference. With this approach, sparse component covariance matrices are directly obtained. The framework results in a parsimonious model-based clustering of the data via a flexible model for the within-group joint distribution of the variables. Extensive simulated data experiments and application to illustrative datasets show that the method attains good classification performance and model quality. The general methodology for model-based clustering with sparse covariance matrices is implemented in the R package mixggm, available on CRAN.
266Scopus© Citations 12