A Variational Approximations-DIC Rubric for Parameter Estimation and Mixture Model Selection Within a Family Setting

Subedi, Sanjeena; McNicholas, Paul D.

doi:10.1007/s00357-019-09351-3

Cited by 6 publications

(3 citation statements)

References 98 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In particular, a

K

‐component finite mixture density can be written as

f (y_{i} false| Ω) = {false\sum}_{k = 1}^{K} π_{k} f_{k} (y_{i} false| Ω_{k}),

where,

π_{k} > 0

is the mixing portion such that

\sum_{k = 1}^{K} π_{k} = 1

f_{k} (y_{i} false| Ω_{k})

is the density function of each component, and

Ω = (Ω_{1}, Ω_{2}, \dots, Ω_{K})

represents the model parameters. In the last three decades, there has been an explosion in model‐based approaches for clustering different types of data [4, 9, 11, 12, 35, 46, 51, 52].…”

Section: Introductionmentioning

confidence: 99%

A family of mixture models for biclustering

Subedi

2021

Statistical Analysis

Self Cite

View full text Add to dashboard Cite

Biclustering is used for simultaneous clustering of the observations and variables when there is no group structure known a priori. It is being increasingly used in bioinformatics, text analytics, and so on. Previously, biclustering has been introduced in a model‐based clustering framework by utilizing a structure similar to a mixture of factor analyzers. In such models, observed variables X are modeled using a latent variable U that is assumed to be from Nfalse(0,Ifalse). Clustering of variables are introduced by imposing constraints on the entries of the factor loading matrix to be 0 and 1 that results in block diagonal covariance matrices. However, this approach is overly restrictive as off‐diagonal elements in the blocks of the covariance matrices can only be 1 which can lead to unsatisfactory model fit on complex data. Here, the latent variable U is assumed to be from a Nfalse(0,Tfalse) where T is a diagonal matrix. This ensures that the off‐diagonal terms in the block matrices within the covariance matrices are non‐zero and not restricted to be 1. This leads to a superior model fit on complex data. A family of models is developed by imposing constraints on the components of the covariance matrix. For parameter estimation, an alternating expectation conditional maximization (AECM) algorithm is used. Finally, the proposed method is illustrated using simulated and real datasets.

show abstract

“…In particular, a

K

‐component finite mixture density can be written as

f (y_{i} false| Ω) = {false\sum}_{k = 1}^{K} π_{k} f_{k} (y_{i} false| Ω_{k}),

where,

π_{k} > 0

is the mixing portion such that

\sum_{k = 1}^{K} π_{k} = 1

f_{k} (y_{i} false| Ω_{k})

is the density function of each component, and

Ω = (Ω_{1}, Ω_{2}, \dots, Ω_{K})

represents the model parameters. In the last three decades, there has been an explosion in model‐based approaches for clustering different types of data [4, 9, 11, 12, 35, 46, 51, 52].…”

Section: Introductionmentioning

confidence: 99%

A family of mixture models for biclustering

Subedi

2021

Statistical Analysis

Self Cite

View full text Add to dashboard Cite

show abstract

“…de Souto et al (2008) did a comparative analysis of several clustering techniques on 35 different cancer gene expression datasets and concluded that a mixture model‐based clustering approach showed superior performance in terms of recovering the true structure of the data as opposed to the traditional distance‐based approaches such as k ‐means and hierarchical methods. Model‐based clustering, which utilizes mixture models, has been increasingly used in the last two decades (Bouveyron & Brunet, 2012; Browne & McNicholas, 2015; Dang et al, 2015; Gollini & Murphy, 2014; Kosmidis & Karlis, 2016; Subedi & McNicholas, 2014, 2020; Subedi et al, 2015; Tortora et al, 2019; Vrbik & McNicholas, 2014). A finite mixture model assumes that the population consists of a finite mixture of subpopulations or components, which can be represented by a parametric model.…”

Section: Introductionmentioning

confidence: 99%

A family of parsimonious mixtures of multivariate Poisson‐lognormal distributions for clustering multivariate count data

Subedi

Browne

2020

Stat

Self Cite

View full text Add to dashboard Cite

Multivariate count data are commonly encountered through high‐throughput sequencing technologies in bioinformatics, text mining, or sports analytics. Although the Poisson distribution seems a natural fit to these count data, its multivariate extension is computationally expensive. In most cases, mutual independence among the variables is assumed; however, this fails to take into account the correlation among the variables usually observed in the data. Recently, mixtures of multivariate Poisson‐lognormal (MPLN) models have been used to analyze such multivariate count measurements with a dependence structure. In the MPLN model, each count is modeled using an independent Poisson distribution conditional on a latent multivariate Gaussian variable. Owing to this hierarchical structure, the MPLN model can account for over‐dispersion as opposed to the traditional Poisson distribution and allows for correlation between the variables. Rather than relying on a Monte Carlo‐based estimation framework, which is computationally inefficient, a fast variational expectation–maximization (EM)‐based framework is used here for parameter estimation. Further, a family of parsimonious mixtures of Poisson‐lognormal distributions is proposed by decomposing the covariance matrix and imposing constraints on these decompositions. Utility of such models is shown using simulated and benchmark datasets.

show abstract

“…, θ K ) represents the model parameters. In the last three decades, there has been an explosion in model-based approaches for clustering different types of data (Banfield and Raftery, 1993;Fraley and Raftery, 2002;Subedi and McNicholas, 2014;Franczak et al, 2014;Dang et al, 2015;Melnykov and Zhu, 2018;Silva et al, 2019;Subedi and McNicholas, 2020).…”

Section: Introductionmentioning

confidence: 99%