Theoretical grounding for estimation in conditional independence multivariate finite mixture models

Zhu, Xiaotian; Hunter, David R.

doi:10.1080/10485252.2016.1225049

Cited by 8 publications

(9 citation statements)

References 20 publications

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“…, J). Considering the MSLE is more convenient than considering the maximum likelihood estimate because the MSLE can be obtained by a Majorization-Minimization algorithm (see Levine et al (2011) for details on the algorithm and Zhu and Hunter (2016) for recent developments) implemented in the R package mixtools Benaglia et al (2009).…”

Section: Nonparametric Clustering Of the Regionsmentioning

confidence: 99%

Translation-invariant functional clustering on COVID-19 deaths adjusted on population risk factors

Cheam¹,

Frédette²,

Marbac³

et al. 2020

Preprint

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The COVID-19 pandemic has taken the world by storm with its high infection rate. Investigating its geographical disparities has paramount interest in order to gauge its relationships with political decisions, economic indicators, or mental health. This paper focuses on clustering the daily death rates reported in several regions of Europe and the United States over eight months. Several methods have been developed to cluster such functional data. However, these methods are not translation-invariant and thus cannot handle different times of arrivals of the disease, nor can they consider external covariates and so are unable to adjust for the population risk factors of each region. We propose a novel three-step clustering method to circumvent these issues. As a first step, feature extraction is performed by translation-invariant wavelet decomposition which permits to deal with the different onsets. As a second step, single-index regression is used to neutralize disparities caused by population risk factors. As a third step, a nonparametric mixture is fitted on the regression residuals to achieve the region clustering. Supplementary materials for this article, including a standardized description of the materials available for reproducing the work, are available online.

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Section: Nonparametric Clustering Of the Regionsmentioning

confidence: 99%

Translation-invariant functional clustering on COVID-19 deaths adjusted on population risk factors

Cheam¹,

Frédette²,

Marbac³

et al. 2020

Preprint

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“…We begin by defining some operators that will aid notation. Much of the development of this section follows the recent work of Levine et al (2011) and Zhu and Hunter (2016); the novelty here is in the incorporation of the A j matrices into the usual conditional independence framework, which requires some delicacy.…”

Section: Parameter Estimationmentioning

confidence: 99%

“…(10) Zhu and Hunter (2016) point out that when f is a density on R r , the right side of (10) simplifies because the denominator is 1, and also that the P and S h operators commute, i.e., (P…”

Section: Parameter Estimationmentioning

confidence: 99%

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Clustering via finite nonparametric ICA mixture models

Zhu

Hunter

2018

Adv Data Anal Classif

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We propose a novel extension of nonparametric multivariate finite mixture models by dropping the standard conditional independence assumption and incorporating the independent component analysis (ICA) structure instead. This innovation extends nonparametric mixture model estimation methods to situations in which conditional independence, a necessary assumption for the unique identifiability of the parameters in such models, is clearly violated. We formulate an objective function in terms of penalized smoothed Kullback-Leibler distance and introduce the nonlinear smoothed majorizationminimization independent component analysis (NSMM-ICA) algorithm for optimizing this function and estimating the model parameters. Our algorithm does not require any labeled observations a priori; it may be used for fully unsupervised clustering problems in a multivariate setting. We have implemented a practical version of this algorithm, which utilizes the FastICA algorithm, in the R package icamix. We illustrate this new methodology using several applications in unsupervised learning and image processing.

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“…A full parametric setting is also presented, however if one of the clustering or regression model were ill-specified, its bias modeling could contaminate the results of the other one. Thus we focus on semi-parametric mixture where the component densities are defined as a product of univariate densities (Chauveau et al, 2015;Zhu and Hunter, 2016;Zheng and Wu, 2019), which is identifiable if the univariate densities are linearly independent and if at least three variables are used for clustering (Allman et al, 2009). Note that, mixtures of symmetric distributions (Hunter et al, 2007;Butucea and Vandekerkhove, 2014) could also be considered in a similar way.…”

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confidence: 99%

Simultaneous semi-parametric estimation of clustering and regression

Marbac¹,

Sedki²,

Biernacki³

et al. 2020

Preprint

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We investigate the parameter estimation of regression models with fixed group effects, when the group variable is missing while group related variables are available. This problem involves clustering to infer the missing group variable based on the group related variables, and regression to build a model on the target variable given the group and eventually additional variables. Thus, this problem can be formulated as the joint distribution modeling of the target and of the group related variables. The usual parameter estimation strategy for this joint model is a two-step approach starting by learning the group variable (clustering step) and then plugging in its estimator for fitting the regression model (regression step). However, this approach is suboptimal (providing in particular biased regression estimates) since it does not make use of the target variable for clustering. Thus, we claim for a simultaneous estimation approach of both clustering and regression, in a semi-parametric framework. Numerical experiments illustrate the benefits of our proposition by considering wide ranges of distributions and regression models. The relevance of our new method is illustrated on real data dealing with problems associated with high blood pressure prevention.

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Theoretical grounding for estimation in conditional independence multivariate finite mixture models

Cited by 8 publications

References 20 publications

Translation-invariant functional clustering on COVID-19 deaths adjusted on population risk factors

Translation-invariant functional clustering on COVID-19 deaths adjusted on population risk factors

Clustering via finite nonparametric ICA mixture models

Simultaneous semi-parametric estimation of clustering and regression

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