A modified local quadratic approximation algorithm for penalized optimization problems

Lee, Sangin; Kwon, Sunghoon; Kim, Yongdai

doi:10.1016/j.csda.2015.08.019

Cited by 32 publications

(26 citation statements)

References 23 publications

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“…That is, LASSO automatically deletes unnecessary covariates. LASSO is known to have many desirable properties for regression models with a large number of covariates, and various efficient optimization algorithms are available for linear regression as well as for generalized linear models [ 8 - 10 ]. To our knowledge, this study is the first to develop a logistic LASSO regression model for diagnosing breast cancer based on radiologic findings and CDD.…”

Section: Introductionmentioning

confidence: 99%

Logistic LASSO regression for the diagnosis of breast cancer using clinical demographic data and the BI-RADS lexicon for ultrasonography

Kim

Jeong

et al. 2018

Ultrasonography

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PurposeThe aim of this study was to compare the performance of image analysis for predicting breast cancer using two distinct regression models and to evaluate the usefulness of incorporating clinical and demographic data (CDD) into the image analysis in order to improve the diagnosis of breast cancer.MethodsThis study included 139 solid masses from 139 patients who underwent a ultrasonography-guided core biopsy and had available CDD between June 2009 and April 2010. Three breast radiologists retrospectively reviewed 139 breast masses and described each lesion using the Breast Imaging Reporting and Data System (BI-RADS) lexicon. We applied and compared two regression methods-stepwise logistic (SL) regression and logistic least absolute shrinkage and selection operator (LASSO) regression-in which the BI-RADS descriptors and CDD were used as covariates. We investigated the performances of these regression methods and the agreement of radiologists in terms of test misclassification error and the area under the curve (AUC) of the tests.ResultsLogistic LASSO regression was superior (P<0.05) to SL regression, regardless of whether CDD was included in the covariates, in terms of test misclassification errors (0.234 vs. 0.253, without CDD; 0.196 vs. 0.258, with CDD) and AUC (0.785 vs. 0.759, without CDD; 0.873 vs. 0.735, with CDD). However, it was inferior (P<0.05) to the agreement of three radiologists in terms of test misclassification errors (0.234 vs. 0.168, without CDD; 0.196 vs. 0.088, with CDD) and the AUC without CDD (0.785 vs. 0.844, P<0.001), but was comparable to the AUC with CDD (0.873 vs. 0.880, P=0.141).ConclusionLogistic LASSO regression based on BI-RADS descriptors and CDD showed better performance than SL in predicting the presence of breast cancer. The use of CDD as a supplement to the BI-RADS descriptors significantly improved the prediction of breast cancer using logistic LASSO regression.

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Section: Introductionmentioning

confidence: 99%

Logistic LASSO regression for the diagnosis of breast cancer using clinical demographic data and the BI-RADS lexicon for ultrasonography

Kim

Jeong

et al. 2018

Ultrasonography

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“…. This modification enables the MLQA algorithm to possess the ascent property (Lee et al, 2016). For the readers, we summarize the algorithm in Algorithm 1.…”

Section: Algorithmmentioning

confidence: 99%

“…We show that under some regularity conditions, the MCL is asymptotically equivalent to an oracle type estimator which is selection consistent even when the number of variables is larger than the sample size. We also develop an efficient algorithm for the MCL by applying the concave-convex procedure (Yuille and Rangarajan, 2003) and modified local quadratic approximation algorithm (Lee et al, 2016). We conduct some numerical studies via simulations and data analysis to show that the MCL can perform better than other penalized estimators for the high-dimensional GLM.…”

Section: Introductionmentioning

confidence: 99%

Moderately clipped LASSO for the high-dimensional generalized linear model

Lee

Kown

2020

CSAM

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The least absolute shrinkage and selection operator (LASSO) is a popular method for a high-dimensional regression model. LASSO has high prediction accuracy; however, it also selects many irrelevant variables. In this paper, we consider the moderately clipped LASSO (MCL) for the high-dimensional generalized linear model which is a hybrid method of the LASSO and minimax concave penalty (MCP). The MCL preserves advantages of the LASSO and MCP since it shows high prediction accuracy and successfully selects relevant variables. We prove that the MCL achieves the oracle property under some regularity conditions, even when the number of parameters is larger than the sample size. An efficient algorithm is also provided. Various numerical studies confirm that the MCL can be a better alternative to other competitors.

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“…One main reason comes from the lack of efficient computational algorithms that implement the penalized estimators. Although there are some unified algorithms studied before (Kwon and Kim, 2012;Lee et al, 2016), data analysts still feel annoying or uncomfortable from working with nonconvex penalties for multinomial logistic regression.…”

Section: Introductionmentioning

confidence: 99%

An efficient algorithm for the non-convex penalized multinomial logistic regression

Kwon

Kim

Lee

2020

CSAM

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In this paper, we introduce an efficient algorithm for the non-convex penalized multinomial logistic regression that can be uniformly applied to a class of non-convex penalties. The class includes most non-convex penalties such as the smoothly clipped absolute deviation, minimax concave and bridge penalties. The algorithm is developed based on the concave-convex procedure and modified local quadratic approximation algorithm. However, usual quadratic approximation may slow down computational speed since the dimension of the Hessian matrix depends on the number of categories of the output variable. For this issue, we use a uniform bound of the Hessian matrix in the quadratic approximation. The algorithm is available from the R package ncpen developed by the authors. Numerical studies via simulations and real data sets are provided for illustration.

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A modified local quadratic approximation algorithm for penalized optimization problems

Cited by 32 publications

References 23 publications

Logistic LASSO regression for the diagnosis of breast cancer using clinical demographic data and the BI-RADS lexicon for ultrasonography

Logistic LASSO regression for the diagnosis of breast cancer using clinical demographic data and the BI-RADS lexicon for ultrasonography

Moderately clipped LASSO for the high-dimensional generalized linear model

An efficient algorithm for the non-convex penalized multinomial logistic regression

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