Mixtures of Shifted AsymmetricLaplace Distributions

Franczak, Brian C.; Browne, Ryan P.; McNicholas, Paul D.

doi:10.1109/tpami.2013.216

Cited by 139 publications

(86 citation statements)

References 51 publications

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“…While this is obvious by inspection in two dimensions, it would be difficult to detect in higher dimensions. The unsuitability of Gaussian mixtures for capturing asymmetric clusters via a posteriori merging has been noted previously (e.g., Franczak et al 2014;Murray et al 2014a). This is one reason why it has been said that merging Gaussian components is not a "get out of jail free" card (McNicholas and Browne 2013).…”

Section: Mixtures Of Asymmetric Componentsmentioning

confidence: 71%

“…A little about these will be said at the end of this section; however, the focus here will be on mixtures of distributions that arise as special or limiting cases of the generalized hyperbolic distribution. Franczak et al (2014) use a mixture of shifted asymmetric Laplace (SAL) distributions for clustering. The density of a random variable X from a p-dimensional SAL distribution is given by…”

Section: Mixtures Of Asymmetric Componentsmentioning

confidence: 99%

“…where W Exp(1) and V N(0, Σ) is independent of W (Kotz, Kozubowski, and Podgorski 2001;Franczak et al 2014). It follows that W | x has a generalized inverse Gaussian distribution (Barndorff-Nielsen 1997); accordingly, the E-steps in the associated EM algorithm are highly tractable (see Franczak et al 2014, for details).…”

Section: Mixtures Of Asymmetric Componentsmentioning

confidence: 99%

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Model-Based Clustering

McNicholas

2016

J Classif

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181

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Abstract:The notion of defining a cluster as a component in a mixture model was put forth by Tiedeman in 1955; since then, the use of mixture models for clustering has grown into an important subfield of classification. Considering the volume of work within this field over the past decade, which seems equal to all of that which went before, a review of work to date is timely. First, the definition of a cluster is discussed and some historical context for model-based clustering is provided. Then, starting with Gaussian mixtures, the evolution of model-based clustering is traced, from the famous paper by Wolfe in 1965 to work that is currently available only in preprint form. This review ends with a look ahead to the next decade or so.

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Section: Mixtures Of Asymmetric Componentsmentioning

confidence: 71%

Section: Mixtures Of Asymmetric Componentsmentioning

confidence: 99%

Section: Mixtures Of Asymmetric Componentsmentioning

confidence: 99%

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Model-Based Clustering

McNicholas

2016

J Classif

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181

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“…For example, some work has been done using symmetric component densities that parameterize concentration (tail weight), e.g., the t distribution , Andrews & McNicholas 2011, Lin, McNicholas & Hsiu 2014) and the power exponential distribution (Dang, Browne & McNicholas 2015). There has also been work on mixtures for discrete data (e.g., Karlis & Meligkotsidou 2007, Bouguila & ElGuebaly 2009) as well as several examples of mixtures of skewed distributions such as the NIG distribution (Karlis & Santourian 2009, Subedi & McNicholas 2014, the skew-t distribution (Lin 2010, Vrbik & McNicholas 2012, Lee & McLachlan 2014, 2016, the shifted asymmetric Laplace distribution (Morris & McNicholas 2013, Franczak, Browne & McNicholas 2014, the variance-gamma distribution , the generalized hyperbolic distribution , and others (e.g., Elguebaly & Bouguila 2015, Franczak, Tortora, Browne & McNicholas 2015.…”

Section: Model-based Clustering and Mixture Modelsmentioning

confidence: 99%

A matrix variate skew‐t distribution

Gallaugher

McNicholas

2017

Stat

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Clustering is the process of finding underlying group structures in data. Although mixture model-based clustering is firmly established in the multivariate case, there is a relative paucity of work on matrix variate distributions and none for clustering with mixtures of skewed matrix variate distributions. Four finite mixtures of skewed matrix variate distributions are considered. Parameter estimation is carried out using an expectation-conditional maximization algorithm, and both simulated and real data are used for illustration.

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“…Examples of such models are the multivariate skew Gaussian and t variant FMMs, and the shifted asymmetric Laplace FMM; see Lee and McLachlan (2013) and Franczak et al (2014), respectively.…”

Section: Non-gaussian Mixture Models On R Dmentioning

confidence: 99%

Finite mixture models for regression problems

Nguyen¹

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Finite mixture models (FMMs) are a ubiquitous tool for the analysis of heterogeneous data across a broad number of fields including agriculture, bioinformatics, botany, cell biology, economics, fisheries research, genetics, genomics, geology, machine learning, medicine, palaeontology, psychology, and zoology, among many others. Due to their flexibility, FMMs can be used to cluster data, classify data, estimate densities, and increasingly, they are also being used to conduct regression analysis and to analyze regression outcomes. There is now an expansive literature on the usage of FMMs for regression, as well as a broad demand for the development of such methods for the analysis of new and complex data.This thesis begins with a summary of the current literature on FMMs and their applications to regression problems. Here, the mixture of regression models (MRMs), cluster-weight models (CWMs), mixtures of experts (MoEs), and mixtures of linear of mixed effects models (MLMMs), as well as other variants of FMMs for regression analysis are introduced. Various properties such as denseness and identifiability, as well as maximum likelihood (ML) estimation techniques such as the expectation-maximization (EM) and minorization-maximization (MM) algorithms are discussed, and a review is presented regarding asymptotic inference and model selection in FMMs. A new result on the characterization of a t linear CWM (LCWM) is also presented. Some new applications of FMMs to regression problems are then discussed.Firstly, a series of models based on FMMs are presented for the clustering and classification of sparsely sampled bivariate functional data. These methods are named mixture of spatial spline regression (MSSR) and MSSR discriminant analysis (MSSRDA). MSSR is constructed using the theory of MLMMs and spatial splines, and an EM algorithm for the ML estimation of the model is presented. MSSRDA is then constructed by combining MSSR with the mixture discriminant analysis framework for classification. The methods are tested on their ability to cluster and classify simulated data. An example application to handwritten digits recognition is then presented. Here, it is shown that MSSR and MSSRDA perform comparably to currently available methods, and outperform said methods in missing data scenarios.Secondly, an FMM is used to produce a false discovery rate (FDR) control procedure for magnetic resonance imaging (MRI) data. In MRI data analysis, millions of hypotheses are often tested simultaneously, resulting in inflated numbers of false positive results. Many of the available FDR techniques for MRI data either do not take into account the spatial structure or rely on difficult to verify assumptions and user-specified parameters. To address these shortcomings, the Markov random field (MRF) FDR (MRF-FDR) technique is presented. MRF-FDR uses a Gaussian mixture model (GMM) to perform FDR control based on empirical-Bayesian principles. An MRF is then used to make the outcome of the GMM spatially coherent. The MRF is fitted using ...

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Mixtures of Shifted AsymmetricLaplace Distributions

Cited by 139 publications

References 51 publications

Model-Based Clustering

Model-Based Clustering

A matrix variate skew‐t distribution

Finite mixture models for regression problems

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