Regularized multivariate regression models with skew-t error distributions

Chen, Lianfu; Pourahmadi, Mohsen; Maadooliat, Mehdi

doi:10.1016/j.jspi.2014.02.001

Cited by 19 publications

(9 citation statements)

References 33 publications

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“…First, other penalty functions for multivariate model estimations can be applied, such as master predictor penalty, 36 L 2 SVS, 37 and L ∞ SVS 38 . Second, the assumption of a multivariate normal distribution on

Y_{i}

can be extended to other distributions, such as the multivariate skew‐normal distribution 39 and the multivariate skew‐ t distribution, 40 to allow the presence of skewness and kurtosis in data. Third, missing values in the GDSC data were imputed by random forest imputation algorithm.…”

Section: Discussionmentioning

confidence: 99%

Generalized finite mixture of multivariate regressions with applications to therapeutic biomarker identification

Rao

2020

Statistics in Medicine

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Finite mixtures of regressions have been used to analyze data that come from a heterogeneous population. When more than one response is observed, accommodating a multivariate response can be useful. In this article, we go a step further and introduce a multivariate extension that includes a latent overlapping cluster indicator variable that allows for potential overdispersion. A generalized mixture of multivariate regressions in connection with the proposed model and a new EM algorithm for fitting are provided. In addition, we allow for high-dimensional predictors via shrinkage estimation. This model proves particularly useful in the analysis of complex data like the search for cancer therapeutic biomarkers. We demonstrate this using the genomics of drug sensitivity in cancer resource.

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Y_{i}

Section: Discussionmentioning

confidence: 99%

Generalized finite mixture of multivariate regressions with applications to therapeutic biomarker identification

Rao

2020

Statistics in Medicine

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“…Because the RR estimate is well-defined, including the case when the predictors are collinear, we use its

-norm to scale the convergence criterion for our regression coefficient matrix

. In addition, we use the sample covariance matrix of the RR residual to scale the convergence of the precision matrix ( Chen et al , 2014 ). This implies that the convergence criteria for

and

are met when

and

, respectively.…”

Section: Methodsmentioning

confidence: 99%

L2,1-norm regularized multivariate regression model with applications to genomic prediction

2021

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Motivation Genomic selection (GS) is currently deemed the most effective approach to speed up breeding of agricultural varieties. It has been recognized that consideration of multiple traits in GS can improve accuracy of prediction for traits of low heritability. However, since GS forgoes statistical testing with the idea of improving predictions, it does not facilitate mechanistic understanding of the contribution of particular single nucleotide polymorphisms (SNP). Results Here we propose a L2,1-norm regularized multivariate regression model and devise a fast and efficient iterative optimization algorithm, called L2,1-joint, applicable in multi-trait GS. The usage of the L2,1-norm facilitates variable selection in a penalized multivariate regression that considers the relation between individuals, when the number of SNPs is much larger than the number of individuals. The capacity for variable selection allows us to define master regulators that can be used in a multi-trait GS setting to dissect the genetic architecture of the analyzed traits. Our comparative analyses demonstrate that the proposed model is a favorable candidate compared to existing state-of-the-art approaches. Prediction and variable selection with data sets from Brassica napus, wheat and Arabidopsis thaliana diversity panels are conducted to further showcase the performance of the proposed model. Availability and implementation The model is implemented using R programming language and the code is freely available from https://github.com/alainmbebi/L21-norm-GS. Supplementary information Supplementary data are available at Bioinformatics online.

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“…This method could be used to explore associations between SNPs and neuroimaging measures by separately estimating individual neuroimaging measures based on a set of SNPs under study. In our experiments, we firstly conducted RMRR between p SNPs and q ROIs to select top SNPs using all the neuroimaging features (Chen et al 2014). Particularly, the top SNPs were selected based on the absolute values of the regression coefficient matrix row-by-row.…”

Section: Methodsmentioning

confidence: 99%

A Robust Reduced Rank Graph Regression Method for Neuroimaging Genetic Analysis

2018

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To characterize associations between genetic and neuroimaging data, a variety of analytic methods have been proposed in neuroimaging genetic studies. These methods have achieved promising performance by taking into account inherent correlation in either the neuroimaging data or the genetic data alone. In this study, we propose a novel robust reduced rank graph regression based method in a linear regression framework by considering correlations inherent in neuroimaging data and genetic data jointly. Particularly, we model the association analysis problem in a reduced rank regression framework with the genetic data as a feature matrix and the neuroimaging data as a response matrix by jointly considering correlations among the neuroimaging data as well as correlations between the genetic data and the neuroimaging data. A new graph representation of genetic data is adopted to exploit their inherent correlations, in addition to robust loss functions for both the regression and the data representation tasks, and a square-root-operator applied to the robust loss functions for achieving adaptive sample weighting. The resulting optimization problem is solved using an iterative optimization method whose convergence has been theoretically proved. Experimental results on the Alzheimer’s Disease Neuroimaging Initiative (ADNI) dataset have demonstrated that our method could achieve competitive performance in terms of regression performance between brain structural measures and the Single Nucleotide Polymorphisms (SNPs), compared with state-of-the-art alternative methods.

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Regularized multivariate regression models with skew-t error distributions

Cited by 19 publications

References 33 publications

Generalized finite mixture of multivariate regressions with applications to therapeutic biomarker identification

Generalized finite mixture of multivariate regressions with applications to therapeutic biomarker identification

L2,1-norm regularized multivariate regression model with applications to genomic prediction

A Robust Reduced Rank Graph Regression Method for Neuroimaging Genetic Analysis

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