Least angle regression for model selection

Zhang, Hongyang; Zamar, Ruben H.

doi:10.1002/wics.1288

Cited by 13 publications

(4 citation statements)

References 47 publications

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“…Deviation from Hardy–Weinberg equilibrium (HWE) was tested using χ 2 test and allele frequencies were estimated. Least angle regression (LARS) analysis was used as regression model selection technique due to its advantages in speed, interpretability and predictive accuracy 34 . In the current study, the dependent variable was BMI.…”

Section: Methodsmentioning

confidence: 99%

“…In those cases, where there was no significant association and due to the limited frequency of the variant allele, homozygotes of the minor allele (aa) and heterozygotes (Aa) were grouped and compared with major allele homozygotes (AA). Stagewise regression and Lasso were also performed to confirm the selection of the independent variables established by LARS 34 . The independent variables selected by LARS method were combined to generate the regression function.…”

Section: Methodsmentioning

confidence: 99%

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Phenotype and genotype predictors of BMI variability among European adults

et al. 2018

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Background/ObjectiveObesity is a complex and multifactorial disease resulting from the interactions among genetics, metabolic, behavioral, sociocultural and environmental factors. In this sense, the aim of the present study was to identify phenotype and genotype variables that could be relevant determinants of body mass index (BMI) variability.Subjects/MethodsIn the present study, a total of 1050 subjects (798 females; 76%) were included. Least angle regression (LARS) analysis was used as regression model selection technique, where the dependent variable was BMI and the independent variables were age, sex, energy intake, physical activity level, and 16 polymorphisms previously related to obesity and lipid metabolism.ResultsThe LARS analysis obtained the following formula for BMI explanation: (64.7 + 0.10 × age [years] + 0.42 × gender [0, men; 1, women] + −40.6 × physical activity [physical activity level] + 0.004 × energy intake [kcal] + 0.74 × rs9939609 [0 or 1–2 risk alleles] + −0.72 × rs1800206 [0 or 1–2 risk alleles] + −0.86 × rs1801282 [0 or 1–2 risk alleles] + 0.87 × rs429358 [0 or 1–2 risk alleles]. The multivariable regression model accounted for 21% of the phenotypic variance in BMI. The regression model was internally validated by the bootstrap method (r2 original data set = 0.208, mean r2 bootstrap data sets = 0.210).ConclusionIn conclusion, age, physical activity, energy intake and polymorphisms in FTO, APOE, PPARG and PPARA genes are significant predictors of the BMI trait.

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Section: Methodsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

Phenotype and genotype predictors of BMI variability among European adults

et al. 2018

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“…We employ least angle regression (LAR) [80,81], a powerful regularized regression technique that promotes sparsity in the PCE coefficient vectors. Regressors are penalized in such a way that only the most dominant ones are retained.…”

Section: Polynomial Chaos Expansionsmentioning

confidence: 99%

Principal component analysis and sparse polynomial chaos expansions for global sensitivity analysis and model calibration: Application to urban drainage simulation

Nagel

Rieckermann

Sudret

2020

Reliability Engineering & System Safety

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This paper presents an efficient surrogate modeling strategy for the uncertainty quantification and Bayesian calibration of a hydrological model. In particular, a process-based dynamical urban drainage simulator that predicts the discharge from a catchment area during a precipitation event is considered. The goal is to perform a global sensitivity analysis and to identify the unknown model parameters as well as the measurement and prediction errors. These objectives can only be achieved by cheapening the incurred computational costs, that is, lowering the number of necessary model runs. With this in mind, a regularity-exploiting metamodeling technique is proposed that enables fast uncertainty quantification. Principal component analysis is used for output dimensionality reduction and sparse polynomial chaos expansions are used for the emulation of the reduced outputs. Sensitivity measures such as the Sobol indices are obtained directly from the expansion coefficients. Bayesian inference via Markov chain Monte Carlo posterior sampling is drastically accelerated.The quantification of uncertainty has become an integral aspect of computational science and engineering in the last two decades [1,2]. Algorithmic advances on the one hand and hardware improvements on the other hand allow for an increasingly detailed simulation of complex systems.That the underlying models are hardly perfect and the model parameters are barely known with certainty prompts scientist and engineers to conduct an end-to-end analysis of the encountered errors. This process, for which one commonly relies on probability theory, is known as uncertainty quantification (UQ).

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“…Other possibilites are the lasso (Tibshirani, 1996) and least angle regression (see Efron et al, 2004). For a review of the literature dealing with least angle regression, see Zhang and Zamar (2014). But a limitation of all of these methods is that they do not provide an indication of the strength of the empirical evidence that a decision can be made about which independent variable is most important.…”

Section: Introductionmentioning

confidence: 99%

An inferential method for determining which of two independent variables is most important when there is curvature

Wilcox

2018

J. Mod. Appl. Stat. Methods

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Consider three random variables Y, X1 and X2, where the typical value of Y, given X1 and X2, is given by some unknown function m(X1, X2). A goal is to determine which of the two independent variables is most important when both variables are included in the model. Let τ1 denote the strength of the association associated with Y and X1, when X2 is included in the model, and let τ2 be defined in an analogous manner. If it is assumed that m(X1, X2) is given by Y = β0 + β1X1 + β2X2 for some unknown parameters β0, β1 and β2, a robust method for testing H0 : τ1 = τ2 is now available. However, the usual linear model might not provide an adequate approximation of the regression surface. Many smoothers (nonparametric regression estimators) were proposed for estimating the regression surface in a more flexible manner. A robust method is proposed for assessing the strength of the empirical evidence that a decision can be made about which independent variable is most important when using a smoother. The focus is on LOESS, but it is readily extended to any nonparametric regression estimator of interest.

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Least angle regression for model selection

Cited by 13 publications

References 47 publications

Phenotype and genotype predictors of BMI variability among European adults

Phenotype and genotype predictors of BMI variability among European adults

Principal component analysis and sparse polynomial chaos expansions for global sensitivity analysis and model calibration: Application to urban drainage simulation

An inferential method for determining which of two independent variables is most important when there is curvature

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