Robust mixture regression model fitting by Laplace distribution

Song, Weixing; Yao, Weixin; Xing, Yao‐Wu

doi:10.1016/j.csda.2013.06.022

Cited by 86 publications

(78 citation statements)

References 12 publications

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“…It was recently studied by Bai et al (2012) and Song et al (2014) by using robust regression mixture models based on, respectively, the t distribution and the Laplace distribution. In the tone perception experiment, a pure fundamental tone was played to a trained musician.…”

Section: Tone Perception Data Setmentioning

confidence: 99%

“…, 150) as the "strech ratio" variables and the covariates x i = r i = (1, x i ) T where x i is the "tuned" variable of the ith observation. We also follow the study in Bai et al (2012) and Song et al (2014) by using two mixture components. The model selection results, given later in Table 5, confirm twocomponents are present in the data when using the TMoE model and the Bayesian Information Criterion (Schwarz, 1978).…”

Section: Tone Perception Data Setmentioning

confidence: 99%

“…But the one of the NMoE differs slightly from the one of the LMoE and the one of the TMoE (which are quasi-identical), and which, upon a visual inspection, can be seen more adapted by better fitting the two regression lines to the data. The two regression lines may correspond to correct tuning and tuning to the first overtone, respectively, as analyzed in Bai et al (2012) (also see Song et al (2014) for the analysis). The predictor x is the actual tone ratio and the response y is the perceived tone ratio.…”

Section: Tone Perception Data Setmentioning

confidence: 99%

“…In the same context of regression, Song et al (2014) proposed the mixture of Laplace regressions, which has been then extended by Nguyen and McLachlan (2016) to the case of mixture of experts, by introducing the Laplace mixture of linear experts (LMoLE). 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%

“…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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Section: Tone Perception Data Setmentioning

confidence: 99%

Section: Tone Perception Data Setmentioning

confidence: 99%

Section: Tone Perception Data Setmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Robust mixture of experts modeling using thetdistribution

Chamroukhi¹

2016

Neural Networks

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A new method for robust mixture regression

Yao

Chen

2016

Can J Statistics

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Finite mixture regression models have been widely used for modelling mixed regression relationships arising from a clustered and thus heterogenous population. The classical normal mixture model, despite its simplicity and wide applicability, may fail in the presence of severe outliers. Using a sparse, case-specific, and scale-dependent mean-shift mixture model parameterization, we propose a robust mixture regression approach for simultaneously conducting outlier detection and robust parameter estimation. A penalized likelihood approach is adopted to induce sparsity among the mean-shift parameters so that the outliers are distinguished from the remainder of the data, and a generalized Expectation-Maximization (EM) algorithm is developed to perform stable and efficient computation. The proposed approach is shown to have strong connections with other robust methods including the trimmed likelihood method and M-estimation approaches. In contrast to several existing methods, the proposed methods show outstanding performance in our simulation studies.

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Robust structured heterogeneity analysis approach for high‐dimensional data

Sun

Luo

Fan

2022

Statistics in Medicine

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Revealing relationships between genes and disease phenotypes is a critical problem in biomedical studies. This problem has been challenged by the heterogeneity of diseases. Patients of a perceived same disease may form multiple subgroups, and different subgroups have distinct sets of important genes. It is hence imperative to discover the latent subgroups and reveal the subgroup‐specific important genes. Some heterogeneity analysis methods have been proposed in the recent literature. Despite considerable successes, most of the existing studies are still limited as they cannot accommodate data contamination and ignore the interconnections among genes. Aiming at these shortages, we develop a robust structured heterogeneity analysis approach to identify subgroups, select important genes as well as estimate their effects on the phenotype of interest. Possible data contamination is accommodated by employing the Huber loss function. A sparse overlapping group lasso penalty is imposed to conduct regularization estimation and gene identification, while taking into account the possibly overlapping cluster structure of genes. This approach takes an iterative strategy in the similar spirit of K‐means clustering. Simulations demonstrate that the proposed approach outperforms alternatives in revealing the heterogeneity and selecting important genes for each subgroup. The analysis of Cancer Cell Line Encyclopedia data leads to biologically meaningful findings with improved prediction and grouping stability.

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Robust mixture regression model fitting by Laplace distribution

Cited by 86 publications

References 12 publications

Robust mixture of experts modeling using thetdistribution

Robust mixture of experts modeling using thetdistribution

A new method for robust mixture regression

Robust structured heterogeneity analysis approach for high‐dimensional data

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