Robust mixture modeling using the skew t distribution

Lin, Tsung‐I; Lee, Jack C.; Hsieh, Wan J.

doi:10.1007/s11222-006-9005-8

Cited by 185 publications

(114 citation statements)

References 18 publications

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“…By design, our STNMIX model is computationally faster to fit than the skew t mixture (STMIX) model [3,12,16,17] without sacrificing precision or rigor. Ho et al [13] summarized the differences between the STMIX and STNMIX models and showed the implementation of the STNMIX model is generally much simpler and faster than that of STMIX model.…”

Section: Resultsmentioning

confidence: 99%

Parametric modeling of cellular state transitions as measured with flow cytometry

Pyne

Haase

et al. 2011

2011 IEEE 1st International Conference on Computational Advances in Bio and Medical Sciences (ICCABS)

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Background: Gradual or sudden transitions among different states as exhibited by cell populations in a biological sample under particular conditions or stimuli can be detected and profiled by flow cytometric time course data. Often such temporal profiles contain features due to transient states that present unique modeling challenges. These could range from asymmetric non-Gaussian distributions to outliers and tail subpopulations, which need to be modeled with precision and rigor. Results: To ensure precision and rigor, we propose a parametric modeling framework StateProfiler based on finite mixtures of skew t-Normal distributions that are robust against non-Gaussian features caused by asymmetry and outliers in data. Further, we present in StateProfiler a new greedy EM algorithm for fast and optimal model selection. The parsimonious approach of our greedy algorithm allows us to detect the genuine dynamic variation in the key features as and when they appear in time course data. We also present a procedure to construct a wellfitted profile by merging any redundant model components in a way that minimizes change in entropy of the resulting model. This allows precise profiling of unusually shaped distributions and less well-separated features that may appear due to cellular heterogeneity even within clonal populations.

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Section: Resultsmentioning

confidence: 99%

Parametric modeling of cellular state transitions as measured with flow cytometry

Pyne

Haase

et al. 2011

2011 IEEE 1st International Conference on Computational Advances in Bio and Medical Sciences (ICCABS)

Self Cite

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“…This has been shown in terms of density modeling and cluster analysis for multivariate data (Mclachlan and Peel, 1998;Peel and Mclachlan, 2000) as well as for univariate data by using a skewed-t mixture model (Lin et al, 2007). The t-distribution with location parameter µ ∈ R, scale parameter σ 2 ∈ (0, ∞) and degrees of freedom ν ∈ (0, ∞) has the probability density function…”

Section: The T Distributionmentioning

confidence: 93%

“…Lin et al (2007) proposed a mixture of skew t distributions to deal with heavy-tailed and asymmetric distributions. However, in the skew-t mixture model of Lin et al (2007), the mixing proportions and the components means are constant and are not predictor-depending and hence doest not consider the regression problem and is not a mixture of experts model. Wei (2012) considered the t-mixture model for the regression context on univariate data where the means µ k in (13) are (linear) regression functions of the form µ(x; β k ).…”

Section: The T Moe (Tmoe) Modelmentioning

confidence: 99%

“…It has been considered to develop the t mixture model proposed by Mclachlan and Peel (1998) for robust cluster analysis of multivariate data. We also mention that Lin et al (2007) also proposed a mixture of skew t distributions to deal with heavy-tailed and asymmetric distributions. However, in the skew-t mixture model of Lin et al (2007), the mixing proportions and the components means are constant, that is, they are not predictor-depending.…”

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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“…Due to the usefulness of the FM models, many kinds of different FM models were introduced in the past decade via considering various mixture components. For example, see the article by Lin et al (2007) and Lin (2010) and monographs by McLachlan and Basford (1988) , Frühwirth-Schnatter (2006).…”

Section: Introductionmentioning

confidence: 99%

On the Finite Mixture Modelling via Normal Mean-variance Birnbaum-Saunders Distribution

Naderi¹,

Arabpour²,

Jamalizadeh³

2017

JIRSS

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Abstract. This paper presents a new finite mixture model using the normal meanvariance mixture of Birnbaum-Saunders distribution. The proposed model is multimodal with wider ranges of skewness and kurtosis. Moreover, it is useful for modeling highly asymmetric data in various theoretical and applied statistical problems. The maximum likelihood estimates of the parameters of the model are computed iteratively by feasible EM algorithm. To illustrate the finite sample properties and performance of the estimators, we conduct a simulation study and illustrate the usefulness of the new model by analyzing a real dataset.

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Robust mixture modeling using the skew t distribution

Cited by 185 publications

References 18 publications

Parametric modeling of cellular state transitions as measured with flow cytometry

Parametric modeling of cellular state transitions as measured with flow cytometry

Robust mixture of experts modeling using thetdistribution

On the Finite Mixture Modelling via Normal Mean-variance Birnbaum-Saunders Distribution

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