scholarly journals Analytic and bootstrap-after-cross-validation methods for selecting penalty parameters of high-dimensional M-estimators

2022 ◽  
Fractals ◽  
2018 ◽  
Vol 26 (04) ◽  
pp. 1850084 ◽  
Author(s):  
FAJIE WANG ◽  
WEN CHEN ◽  
CHUANZENG ZHANG ◽  
QINGSONG HUA

This study proposes the radial basis function (RBF) based on the Hausdorff fractal distance and then applies it to develop the Kansa method for the solution of the Hausdorff derivative Poisson equations. The Kansa method is a meshless global technique promising for high-dimensional irregular domain problems. It is, however, noted that the shape parameter of the RBFs can have a significant influence on the accuracy and robustness of the numerical solution. Based on the leave-one-out cross-validation algorithm proposed by Rippa, this study presents a new technique to choose the optimal shape parameter of the RBFs with the Hausdorff fractal distance. Numerical experiments show that the Kansa method based on the Hausdorff fractal distance is highly accurate and computationally efficient for the Hausdorff derivative Poisson equations.


2012 ◽  
Vol 11 ◽  
pp. CIN.S9048 ◽  
Author(s):  
Shuhei Kaneko ◽  
Akihiro Hirakawa ◽  
Chikuma Hamada

Mining of gene expression data to identify genes associated with patient survival is an ongoing problem in cancer prognostic studies using microarrays in order to use such genes to achieve more accurate prognoses. The least absolute shrinkage and selection operator (lasso) is often used for gene selection and parameter estimation in high-dimensional microarray data. The lasso shrinks some of the coefficients to zero, and the amount of shrinkage is determined by the tuning parameter, often determined by cross validation. The model determined by this cross validation contains many false positives whose coefficients are actually zero. We propose a method for estimating the false positive rate (FPR) for lasso estimates in a high-dimensional Cox model. We performed a simulation study to examine the precision of the FPR estimate by the proposed method. We applied the proposed method to real data and illustrated the identification of false positive genes.


2020 ◽  
Vol 43 (1) ◽  
pp. 103-125
Author(s):  
Yi Zhong ◽  
Jianghua He ◽  
Prabhakar Chalise

With the advent of high throughput technologies, the high-dimensional datasets are increasingly available. This has not only opened up new insight into biological systems but also posed analytical challenges. One important problem is the selection of informative feature-subset and prediction of the future outcome. It is crucial that models are not overfitted and give accurate results with new data. In addition, reliable identification of informative features with high predictive power (feature selection) is of interests in clinical settings. We propose a two-step framework for feature selection and classification model construction, which utilizes a nested and repeated cross-validation method. We evaluated our approach using both simulated data and two publicly available gene expression datasets. The proposed method showed comparatively better predictive accuracy for new cases than the standard cross-validation method.


2008 ◽  
Vol 26 (3) ◽  
pp. 275-292 ◽  
Author(s):  
Geng Cui ◽  
Man Leung Wong ◽  
Guichang Zhang ◽  
Lin Li

PurposeThe purpose of this paper is to assess the performance of competing methods and model selection, which are non‐trivial issues given the financial implications. Researchers have adopted various methods including statistical models and machine learning methods such as neural networks to assist decision making in direct marketing. However, due to the different performance criteria and validation techniques currently in practice, comparing different methods is often not straightforward.Design/methodology/approachThis study compares the performance of neural networks with that of classification and regression tree, latent class models and logistic regression using three criteria – simple error rate, area under the receiver operating characteristic curve (AUROC), and cumulative lift – and two validation methods, i.e. bootstrap and stratified k‐fold cross‐validation. Systematic experiments are conducted to compare their performance.FindingsThe results suggest that these methods vary in performance across different criteria and validation methods. Overall, neural networks outperform the others in AUROC value and cumulative lifts, and the stratified ten‐fold cross‐validation produces more accurate results than bootstrap validation.Practical implicationsTo select predictive models to support direct marketing decisions, researchers need to adopt appropriate performance criteria and validation procedures.Originality/valueThe study addresses the key issues in model selection, i.e. performance criteria and validation methods, and conducts systematic analyses to generate the findings and practical implications.


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