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An adaptive shortest-solution guided decimation approach to sparse high-dimensional linear regression.

ABSTRACT: High-dimensional linear regression model is the most popular statistical model for high-dimensional data, but it is quite a challenging task to achieve a sparse set of regression coefficients. In this paper, we propose a simple heuristic algorithm to construct sparse high-dimensional linear regression models, which is adapted from the shortest-solution guided decimation algorithm and is referred to as ASSD. This algorithm constructs the support of regression coefficients under the guidance of the shortest least-squares solution of the recursively decimated linear models, and it applies an early-stopping criterion and a second-stage thresholding procedure to refine this support. Our extensive numerical results demonstrate that ASSD outperforms LASSO, adaptive LASSO, vector approximate message passing, and two other representative greedy algorithms in solution accuracy and robustness. ASSD is especially suitable for linear regression problems with highly correlated measurement matrices encountered in real-world applications.

SUBMITTER: Yu X

PROVIDER: S-EPMC8674299 | biostudies-literature | 2021 Dec

REPOSITORIES: biostudies-literature

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An adaptive shortest-solution guided decimation approach to sparse high-dimensional linear regression.

Yu Xue X Sun Yifan Y Zhou Hai-Jun HJ

Scientific reports 20211215 1

High-dimensional linear regression model is the most popular statistical model for high-dimensional data, but it is quite a challenging task to achieve a sparse set of regression coefficients. In this paper, we propose a simple heuristic algorithm to construct sparse high-dimensional linear regression models, which is adapted from the shortest-solution guided decimation algorithm and is referred to as ASSD. This algorithm constructs the support of regression coefficients under the guidance of th ...[more]

PMID: 34911986

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Project description:PurposeThe ICRU/GEC-ESTRO released the ICRU Report No. 89, which introduced the concept of four-dimensional brachytherapy and ushered in a new era of brachytherapy for cervical cancer. The purpose of this study was to evaluate the local control and late toxicity of four-dimensional brachytherapy in cervical cancer through a systematic review and to reveal the dose-response relationship between the volumetric dose paraments and the local control rate via a probit model.Material and methodsWe identified studies that reported the HR-CTV D90 and local control probabilities by searching the PubMed Database, the Web of Science Core Collection and the Cochrane Library Database through February 1st, 2022. Regression analyses were performed between the HR-CTV D90 and the local control probability using a probit model.ResultsNineteen studies enrolling 3,616 patients were included. The probit model showed a significant relationship between the HR-CTV D90 value and IR-CTV D90 Vs. the local control probability, P < 0.001 and P = 0.003, respectively. The D90 for HR-CTV and IR-CTV corresponding to a probability of 90% local control was 79.1 GyEQD2,10 (95% CI:69.8 - 83.7 GyEQD2,10) and 66.5 GyEQD2,10 (95% CI: 62.8 - 67.9 GyEQD2,10), respectively. The limits for the prescribed dose of 85 GyEQD2,10 for HR-CTV D90 theoretically warranted a 92.1% (95% CI: 90.2% - 95.3%) local control rate, and 87.2% (95% CI: 82.4% - 91.8%) local control probability was expected for 65 GyEQD2,10 to IR-CTV D90. The probit model showed no significant relationship between the D2cc to organs at risk and the probability of grade 3 and above gastrointestinal or genitourinary toxicity.ConclusionsFour-dimensional brachytherapy takes into account uncertain factors such as tumour regression, internal organ motion and organ filling, and provides a more accurate and more therapeutic ratio delivery through adaptive delineation and replanning, replacement of the applicator, and the addition of interstitial needles. The dose volume effect relationship of four-dimensional brachytherapy between the HR-CTV D90 and the local control rate provides an objective planning aim dose.

Dataset Information

An adaptive shortest-solution guided decimation approach to sparse high-dimensional linear regression.

Publications

An adaptive shortest-solution guided decimation approach to sparse high-dimensional linear regression.

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