Multivariate Response and Parsimony for Gaussian Cluster-Weighted Models

Dang, Utkarsh J.; Punzo, Antonio; McNicholas, Paul D.; Ingrassia, Salvatore; Browne, Ryan P.

doi:10.1007/s00357-017-9221-2

Cited by 63 publications

(39 citation statements)

References 78 publications

(86 reference statements)

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“…To allow for a direct comparison of the competing models, all the algorithms are initialized by providing the initial quantities

λ z_{i}^{false(0 false)}

i = 1, \dots, n

: nine times using a random initialization and once with a k ‐means initialization (as implemented by the kmeans() function for R). The solution maximizing the observed‐data log‐likelihood among these 10 runs is then selected; see Dang et al (). For alternative initialization strategies, see (Bagnato & Punzo ).…”

Section: Resultsmentioning

confidence: 99%

“…We also evaluate the performance of MLNMs on the ais (Australian Institute of Sports) data set (Cook & Weisberg, ), a real benchmark data set which is often used (in some or all of its variables) for illustration in the model‐based clustering literature (see, e.g., Galimberti and Soffritti, ; Morris et al, ; Murray, Browne, & McNicholas, ; Tortora et al, ; Azzalini et al, ; Dang et al, ). The data set contains measurements on

n = 202

athletes, subdivided in

k = 2

groups (100 female and 102 male), and is available in the R‐packages alr3 (Weisberg, ) and sn (Azzalini, ).…”

Section: Resultsmentioning

confidence: 99%

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The multivariate leptokurtic‐normal distribution and its application in model‐based clustering

2016

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This article proposes the elliptical multivariate leptokurtic‐normal (MLN) distribution to fit data with excess kurtosis. The MLN distribution is a multivariate Gram–Charlier expansion of the multivariate normal (MN) distribution and has a closed‐form representation characterized by one additional parameter denoting the excess kurtosis. It is obtained from the elliptical representation of the MN distribution, by reshaping its generating variate with the associated orthogonal polynomials. The strength of this approach for obtaining the MLN distribution lies in its general applicability as it can be applied to any multivariate elliptical law to get a suitable distribution to fit data. Maximum likelihood is discussed as a parameter estimation technique for the MLN distribution. Mixtures of MLN distributions are also proposed for robust model‐based clustering. An EM algorithm is presented to obtain estimates of the mixture parameters. Benchmark real data are used to show the usefulness of mixtures of MLN distributions. The Canadian Journal of Statistics 45: 95–119; 2017 © 2016 Statistical Society of Canada

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“…To allow for a direct comparison of the competing models, all the algorithms are initialized by providing the initial quantities

λ z_{i}^{false(0 false)}

i = 1, \dots, n

Section: Resultsmentioning

confidence: 99%

n = 202

athletes, subdivided in

k = 2

groups (100 female and 102 male), and is available in the R‐packages alr3 (Weisberg, ) and sn (Azzalini, ).…”

Section: Resultsmentioning

confidence: 99%

The multivariate leptokurtic‐normal distribution and its application in model‐based clustering

2016

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“…Therefore, it could be of interest to evaluate the decision boundaries for mixtures of regressions when, for example, Gaussian assumptions are made about the distribution of Y |x in each mixture component. Finally, always in the case of multiple response variables, parsimonious variants of mixtures of (linear) regressions, under Gaussian assumptions, have been recently proposed by imposing constraints on the eigendecomposed component matrices of Y |x (see Dang & McNicholas, 2015 in the case of fixed covariates and Dang, Punzo, McNicholas, Ingrassia, & Browne, 2014 in the case of random covariates). Also in this case, in line with the studies about linear and quadratic discriminant analysis, it could be of interest to evaluate the impact of these constraints on the resulting decision boundaries.…”

Section: Discussionmentioning

confidence: 99%

Decision boundaries for mixtures of regressions

Ingrassia

Punzo

2016

Journal of the Korean Statistical Society

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a b s t r a c tThe analysis of the decision boundaries plays an important role in understanding the characteristics of a classifier in the framework of model-based clustering and discriminant analysis. The wider is the family of decision boundaries generated by a classifier the larger is its flexibility for classification purposes. In this paper, we present rigorous results concerning the decision boundaries of mixtures of (linear) regressions under Gaussian assumptions. In particular, three types of mixtures of regressions are considered: with fixed covariates, with concomitant variables, and with random covariates. The obtained decision boundaries have a geometrical interpretation in terms hyperquadrics and define a taxonomy of the considered models. Beyond Gaussian assumptions, decision boundaries can be investigated numerically; as an example, we illustrate the case of the t distribution.

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“…However, identifiability results exist for some special cases of this class in the case of a single outcome ( d Y =1). For example, general conditions for identifiability of mixtures of linear models with fixed or random covariates are available . Generalizations of these results to mixtures of GLMs are also available in the case of fixed covariates and in the case of random covariates of a mixed type …”

Section: Methodsmentioning

confidence: 99%

Multivariate generalized hidden Markov regression models with random covariates: Physical exercise in an elderly population

Punzo

Ingrassia

Maruotti

2018

Statistics in Medicine

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A time-varying latent variable model is proposed to jointly analyze multivariate mixed-support longitudinal data. The proposal can be viewed as an extension of hidden Markov regression models with fixed covariates (HMRMFCs), which is the state of the art for modelling longitudinal data, with a special focus on the underlying clustering structure. HMRMFCs are inadequate for applications in which a clustering structure can be identified in the distribution of the covariates, as the clustering is independent from the covariates distribution. Here, hidden Markov regression models with random covariates are introduced by explicitly specifying state-specific distributions for the covariates, with the aim of improving the recovering of the clusters in the data with respect to a fixed covariates paradigm. The hidden Markov regression models with random covariates class is defined focusing on the exponential family, in a generalized linear model framework. Model identifiability conditions are sketched, an expectation-maximization algorithm is outlined for parameter estimation, and various implementation and operational issues are discussed. Properties of the estimators of the regression coefficients, as well as of the hidden path parameters, are evaluated through simulation experiments and compared with those of HMRMFCs. The method is applied to physical activity data.

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Multivariate Response and Parsimony for Gaussian Cluster-Weighted Models

Cited by 63 publications

References 78 publications

The multivariate leptokurtic‐normal distribution and its application in model‐based clustering

The multivariate leptokurtic‐normal distribution and its application in model‐based clustering

Decision boundaries for mixtures of regressions

Multivariate generalized hidden Markov regression models with random covariates: Physical exercise in an elderly population

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