Local Statistical Modeling via a Cluster-Weighted Approach with Elliptical Distributions

Ingrassia, Salvatore; Minotti, Simona C.; Vittadini, Giorgio

doi:10.1007/s00357-012-9114-3

Cited by 118 publications

(125 citation statements)

References 42 publications

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“…CWM was initially introduced under Gaussian and linear assumptions (Gershenfeld et al 1999). The extension to other distributions is treated for example in Ingrassia et al (2012).…”

Section: Tcwrm and Adaptive Tclust-reg: Theoretical And Computationalmentioning

confidence: 99%

Assessing trimming methodologies for clustering linear regression data

Torti

Perrotta

Riani

et al. 2018

Adv Data Anal Classif

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We assess the performance of state-of-the-art robust clustering tools for regression structures under a variety of different data configurations. We focus on two methodologies that use trimming and restrictions on group scatters as their main ingredients. We also give particular care to the data generation process through the development of a flexible simulation tool for mixtures of regressions, where the user can control the degree of overlap between the groups. Level of trimming and restriction factors are input parameters for which appropriate tuning is required. Since we find that incorrect specification of the second-level trimming in the Trimmed CLUSTering REGression model (TCLUST-REG) can deteriorate the performance of the method, we propose an improvement where the second-level trimming is not fixed in advance but is data dependent. We then compare our adaptive version of TCLUST-REG with the Trimmed Cluster Weighted Restricted Model (TCWRM) which provides a powerful extension of the robust clusterwise regression methodology. Our overall conclusion is that the two methods perform comparably, but with notable differences due to the inherent degree of modeling implied by them.

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“…CWM was initially introduced under Gaussian and linear assumptions (Gershenfeld et al 1999). The extension to other distributions is treated for example in Ingrassia et al (2012).…”

Section: Tcwrm and Adaptive Tclust-reg: Theoretical And Computationalmentioning

confidence: 99%

Assessing trimming methodologies for clustering linear regression data

Torti

Perrotta

Riani

et al. 2018

Adv Data Anal Classif

View full text Add to dashboard Cite

show abstract

“…Unlike the case of the standard t mixture model (e.g., Mclachlan and Peel (1998);Peel and Mclachlan (2000)) and t regression mixture model (Wei, 2012;Bai et al, 2012;Ingrassia et al, 2012), for which the mixing proportions are not predictor-depending and their update is done in closed form, for the proposed TMoE does, there is no a a closed form solution to update the gating network parameters. This is performed by Iteratively Reweighted Least Squares (IRLS).…”

Section: M-stepmentioning

confidence: 99%

“…More specifically, we use polynomial regressors for the components, as well as multinomial logistic regressors for the mixing proportions. In the framework of regression analysis, recently, Bai et al (2012); Ingrassia et al (2012) proposed a robust mixture modeling of regression on univariate data, by using a univariate t-mixture model. For the general multivariate case using t mixtures, one can refer to for example the two key papers Mclachlan and Peel (1998); Peel and Mclachlan (2000).…”

Section: Introductionmentioning

confidence: 99%

“…For the Bayesian framework, Frühwirth-Schnatter and Pyne (2010) have considered the Bayesian inference for both the univariate and the multivariate skew-normal and skew-t mixtures. For the regression context, the robust modeling of regression data has been studied namely by Wei (2012) ;Ingrassia et al (2012) who considered a t-mixture model for regression analysis of univariate data, as well as by Bai et al (2012) who relied on the M-estimate in mixture of linear regressions.…”

Section: Introductionmentioning

confidence: 99%

“…However, unlike our proposed TMoE model, the regression mixture models of Wei (2012), Bai et al (2012), Ingrassia et al (2012), and Song et al (2014) do not consider conditional mixing proportions, that is, mixing proportions depending on some input variables, as in the case of mixture of experts, which we investigate here.…”

Section: Introductionmentioning

confidence: 99%

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Robust mixture of experts modeling using thetdistribution

Chamroukhi¹

2016

Neural Networks

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Mixture of Experts (MoE) is a popular framework for modeling heterogeneity in data for regression, classification, and clustering. For regression and cluster analyses of continuous data, MoE usually use normal experts following the Gaussian distribution. However, for a set of data containing a group or groups of observations with heavy tails or atypical observations, the use of normal experts is unsuitable and can unduly affect the fit of the MoE model. We introduce a robust MoE modeling using the t distribution. The proposed t MoE (TMoE) deals with these issues regarding heavy-tailed and noisy data. We develop a dedicated expectation-maximization (EM) algorithm to estimate the parameters of the proposed model by monotonically maximizing the observed data log-likelihood. We describe how the presented model can be used in prediction and in model-based clustering of regression data. The proposed model is validated on numerical experiments carried out on simulated data, which show the effectiveness and the robustness of the proposed model in terms of modeling non-linear regression functions as well as in model-based clustering. Then, it is applied to the real-world data of tone perception for musical data analysis, and the one of temperature anomalies for the analysis of climate change data. The obtained results show the usefulness of the TMoE model for practical applications.

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Multilevel logistic cluster‐weighted model for outcome evaluation in health care*

Berta

Vinciotti

2019

Statistical Analysis

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In health care, multilevel models are typically used to evaluate hospitals' performance and to rank hospitals accordingly. While multilevel models capture the hierarchical structure in the data, such as the grouping of patients into hospitals, these models do not account for additional latent structures. In this paper, we develop a novel multilevel logistic cluster‐weighted model which can predict a binary outcome, such as mortality within 30 days of discharge, while accounting both for known and latent structures of the data. We develop an Expectation‐Maximization algorithm for parameter estimation and a parametric bootstrap approach for assessing the variability of the estimators. Using a rich data set of the Lombardy (Italy) health care system and focussing on the two wards of cardiosurgery and medicine, we show how the proposed model detects, in both cases, two well‐defined clusters within the patient to hospital hierarchical structure of the data. A comparison with standard multilevel and cluster‐weighted approaches reveals a better fit of the proposed model and a greater insight into the structure of the data. We show how this can have implications in the resulting league tables and thus how the proposed model can be a useful tool for policy‐makers and healthcare managers to conduct hospital evaluations.

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Local Statistical Modeling via a Cluster-Weighted Approach with Elliptical Distributions

Cited by 118 publications

References 42 publications

Assessing trimming methodologies for clustering linear regression data

Assessing trimming methodologies for clustering linear regression data

Robust mixture of experts modeling using thetdistribution

Multilevel logistic cluster‐weighted model for outcome evaluation in health care*

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