Regularization and Variable Selection Via the Elastic Net

Zou, Hui; Hastie, Trevor

doi:10.1111/j.1467-9868.2005.00503.x

Cited by 16,020 publications

(12,231 citation statements)

References 23 publications

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“…Elastic net regularization was used to improve prediction accuracy by shrinking the regression coefficients making them more stable and reducing the estimation variance due to possible multicollinearity [49]. Shrinkage occurs through applying a penalty to the regression model.…”

Section: Resultsmentioning

confidence: 99%

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Leg pain and psychological variables predict outcome 2–3 years after lumbar fusion surgery

2011

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Prediction studies testing a thorough range of psychological variables in addition to demographic, workrelated and clinical variables are lacking in lumbar fusion surgery research. This prospective cohort study aimed at examining predictions of functional disability, back pain and health-related quality of life (HRQOL) 2-3 years after lumbar fusion by regressing nonlinear relations in a multivariate predictive model of pre-surgical variables. Before and 2-3 years after lumbar fusion surgery, patients completed measures investigating demographics, work-related variables, clinical variables, functional self-efficacy, outcome expectancy, fear of movement/(re)injury, mental health and pain coping. Categorical regression with optimal scaling transformation, elastic net regularization and bootstrapping were used to investigate predictor variables and address predictive model validity. The most parsimonious and stable subset of pre-surgical predictor variables explained 41.6, 36.0 and 25.6% of the variance in functional disability, back pain intensity and HRQOL 2-3 years after lumbar fusion. Pre-surgical control over pain significantly predicted functional disability and HRQOL. Pre-surgical catastrophizing and leg pain intensity significantly predicted functional disability and back pain while the pre-surgical straight leg raise significantly predicted back pain. Postoperative psychomotor therapy also significantly predicted functional disability while pre-surgical outcome expectations significantly predicted HRQOL. For the median dichotomised classification of functional disability, back pain intensity and HRQOL levels 2-3 years post-surgery, the discriminative ability of the prediction models was of good quality. The results demonstrate the importance of pre-surgical psychological factors, leg pain intensity, straight leg raise and postoperative psychomotor therapy in the predictions of functional disability, back pain and HRQOL-related outcomes.

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Section: Resultsmentioning

confidence: 99%

“…Several regularized regression methods have been developed to overcome the flaws of OLS regression. Zou and Hastie [49] proposed the ''Elastic Net'' regularization method which uses shrinkage of regression coefficients to reduce their variability and provide subset selection of stable predictors (Fig. 1).…”

Section: Discussionmentioning

confidence: 99%

Leg pain and psychological variables predict outcome 2–3 years after lumbar fusion surgery

2011

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“…It is well known that the ℓ 1 -regularization term shrinks many components of the solution to zero, and thus performs feature selection [4]. There has been also some variants, such as elastic nets [5], to select highly-correlated predictive features. The number of selected features in eqn (1) is controlled by the regularization parameter λ.…”

Section: Introductionmentioning

confidence: 99%

Scoring relevancy of features based on combinatorial analysis of Lasso with application to lymphoma diagnosis

et al. 2013

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One challenge in applying bioinformatic tools to clinical or biological data is high number of features that might be provided to the learning algorithm without any prior knowledge on which ones should be used. In such applications, the number of features can drastically exceed the number of training instances which is often limited by the number of available samples for the study. The Lasso is one of many regularization methods that have been developed to prevent overfitting and improve prediction performance in high-dimensional settings. In this paper, we propose a novel algorithm for feature selection based on the Lasso and our hypothesis is that defining a scoring scheme that measures the "quality" of each feature can provide a more robust feature selection method. Our approach is to generate several samples from the training data by bootstrapping, determine the best relevance-ordering of the features for each sample, and finally combine these relevance-orderings to select highly relevant features. In addition to the theoretical analysis of our feature scoring scheme, we provided empirical evaluations on six real datasets from different fields to confirm the superiority of our method in exploratory data analysis and prediction performance. For example, we applied FeaLect, our feature scoring algorithm, to a lymphoma dataset, and according to a human expert, our method led to selecting more meaningful features than those commonly used in the clinics. This case study built a basis for discovering interesting new criteria for lymphoma diagnosis. Furthermore, to facilitate the use of our algorithm in other applications, the source code that implements our algorithm was released as FeaLect, a documented R package in CRAN.

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“…laboratory where for each quality parameter an individual method and equipment is needed. Recently, spectroscopic methods 45 are being developed in order to determine relevant quality parameters simultaneously in much shorter time and strongly 46 reduced effort for sample preparation [5] [6]. In this context, chemometric methods are employed to gain mathematical 47 models for quantification of the analytes [7] and process parameters [8].…”

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confidence: 99%

Improved quantification of important beer quality parameters based on nonlinear calibration methods applied to FT-MIR spectra

Cernuda

Lughofer

Klein³

et al. 2016

Anal Bioanal Chem

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During the production process of beer, it is of utmost importance to guarantee a high consistency of the beer 7 quality. For instance, the bitterness is an essential quality parameter which has to be controlled within the specifications 8 already at the beginning of the production process in the unfermented beer (wort) as well as in final products such as beer 9 and beer mix beverages. Nowadays, analytical techniques for quality control in beer production are mainly based on manual 10 supervision, i.e. samples are taken from the process and analyzed in the laboratory. This typically requires significant lab 11 technicians efforts for only a small fraction of samples to be analyzed, which leads to significant costs for beer breweries and

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Regularization and Variable Selection Via the Elastic Net

Cited by 16,020 publications

References 23 publications

Leg pain and psychological variables predict outcome 2–3 years after lumbar fusion surgery

Leg pain and psychological variables predict outcome 2–3 years after lumbar fusion surgery

Scoring relevancy of features based on combinatorial analysis of Lasso with application to lymphoma diagnosis

Improved quantification of important beer quality parameters based on nonlinear calibration methods applied to FT-MIR spectra

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