Constrained monotone EM algorithms for mixtures of multivariate t distributions

Greselin, Francesca; Ingrassia, Salvatore

doi:10.1007/s11222-008-9112-9

Cited by 38 publications

(17 citation statements)

References 24 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In (1), normality of both p y|x, Ω g and p x|Ω g is commonly assumed (see, e.g., Gershenfeld, 1997 andPunzo, 2014). Alternatively, Ingrassia et al (2012) propose also the use of the t distribution which provides, as other approaches , 2014a, more robust fitting for groups of observations with longer than normal tails or noise data (see, e.g., Zellner, 1976, Lange et al, 1989, Peel & McLachlan, 2000, McLachlan & Peel, 2000, Chapter 7, Chatzis & Varvarigou, 2008, and Greselin & Ingrassia, 2010. In particular, the authors consider p y|x, Ω g = h t y|x; ξ g , ζ g = Γ ζ g + 1 2…”

Section: Introductionmentioning

confidence: 99%

Model-based clustering via linear cluster-weighted models

Ingrassia

Minotti

Punzo

2014

Computational Statistics & Data Analysis

View full text Add to dashboard Cite

A novel family of twelve mixture models with random covariates, nested in the linear t cluster-weighted model (CWM), is introduced for model-based clustering. The linear t CWM was recently presented as a robust alternative to the better known linear Gaussian CWM. The proposed family of models provides a unified framework that also includes the linear Gaussian CWM as a special case. Maximum likelihood parameter estimation is carried out within the EM framework, and both the BIC and the ICL are used for model selection. A simple and effective hierarchical random initialization is also proposed for the EM algorithm. The novel model-based clustering technique is illustrated in some applications to real data. Finally, a simulation study for evaluating the performance of the BIC and the ICL is presented.

show abstract

Section: Introductionmentioning

confidence: 99%

Model-based clustering via linear cluster-weighted models

Ingrassia

Minotti

Punzo

2014

Computational Statistics & Data Analysis

View full text Add to dashboard Cite

show abstract

“…The behaviour of (29) is illustrated in Figure 3. These constraints have been implemented in Ingrassia (2004), Ingrassia and Rocci (2007) and in Greselin and Ingrassia (2010), both for mixtures of multivariate Gaussian distributions and mixtures of multivariate t distributions. We remark that the approach (29) is not scale invariant.…”

Section: Constraints On the Eigenvalues Of The Covariance Matricesmentioning

confidence: 99%

Eigenvalues and constraints in mixture modeling: geometric and computational issues

García-Escudero

Gordaliza

Greselin

et al. 2017

Adv Data Anal Classif

View full text Add to dashboard Cite

This paper presents a review about the usage of eigenvalues restrictions for constrained parameter estimation in mixtures of elliptical distributions according to the likelihood approach. These restrictions serve a twofold purpose: to avoid convergence to degenerate solutions and to reduce the onset of non interesting (spurious) maximizers, related to complex likelihood surfaces. The paper shows how the constraints may play a key role in the theory of Euclidean data clustering. The aim here is to provide a reasoned review of the constraints and their applications, along the contributions of many authors, spanning the literature of the last thirty years.Keywords Mixture Model · EM algorithm · Eigenvalues · Model-based clustering IntroductionFinite mixture distributions play a central role in statistical modelling, as they combine much of the flexibility of non parametric models with nice analytical properties of parametric models, see e.g.

show abstract

“…They automatically guarantee that we are avoiding the |Σ g | → 0 and σ 2 g → 0 cases. These constraints are an extension to CWMs of those introduced in Ingrassia and Rocci (2007), García-Escudero et al (2008) and Greselin and Ingrassia (2010) and go back to Hathaway (1985). The main difference is the asymmetric and different treatment given by the constraints, when modeling the marginal distribution X or when modeling the regression error terms, providing high flexibility to the model.…”

Section: Problem Statementmentioning

confidence: 99%

Robust estimation of mixtures of regressions with random covariates, via trimming and constraints

et al. 2016

Self Cite

View full text Add to dashboard Cite

A robust estimator for a wide family of mixtures of linear regression is presented. Robustness is based on the joint adoption of the Cluster Weighted Model and of an estimator based on trimming and restrictions. The selected model provides the conditional distribution of the response for each group, as in mixtures of regression, and further supplies local distributions for the explanatory variables. A novel version of the restrictions has been devised, under this model, for separately controlling the two sources of variability identified in it. This proposal avoids singularities in the log-likelihood, caused by approximate local collinearity in the explanatory variables or local exact fits in regressions, and reduces the occurrence of spurious local maximizers. In a natural way, due to the interaction between the model and the estimator, the procedure is able to resist the harmful influence of bad leverage points along the estimation of the mixture of regressions, which is still an open issue in the literature. The given methodology defines a well-posed statistical problem, whose estimator exists and is consistent to the corresponding solution of the population optimum, under widely general conditions. A feasible EM algorithm has also been provided to obtain the corresponding estimation. Many simulated examples and two real datasets have been chosen to show the ability of the procedure, on the one hand, to detect anomalous data, and, on the other hand, to identify the real cluster regressions without the influence of contamination.

show abstract

Constrained monotone EM algorithms for mixtures of multivariate t distributions

Cited by 38 publications

References 24 publications

Model-based clustering via linear cluster-weighted models

Model-based clustering via linear cluster-weighted models

Eigenvalues and constraints in mixture modeling: geometric and computational issues

Robust estimation of mixtures of regressions with random covariates, via trimming and constraints

Contact Info

Product

Resources

About