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A polynomial algorithm for best-subset selection problem.

ABSTRACT: Best-subset selection aims to find a small subset of predictors, so that the resulting linear model is expected to have the most desirable prediction accuracy. It is not only important and imperative in regression analysis but also has far-reaching applications in every facet of research, including computer science and medicine. We introduce a polynomial algorithm, which, under mild conditions, solves the problem. This algorithm exploits the idea of sequencing and splicing to reach a stable solution in finite steps when the sparsity level of the model is fixed but unknown. We define an information criterion that helps the algorithm select the true sparsity level with a high probability. We show that when the algorithm produces a stable optimal solution, that solution is the oracle estimator of the true parameters with probability one. We also demonstrate the power of the algorithm in several numerical studies.

SUBMITTER: Zhu J

PROVIDER: S-EPMC7777147 | biostudies-literature | 2020 Dec

REPOSITORIES: biostudies-literature

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A polynomial algorithm for best-subset selection problem.

Zhu Junxian J Wen Canhong C Zhu Jin J Zhang Heping H Wang Xueqin X

Proceedings of the National Academy of Sciences of the United States of America 20201216 52

Best-subset selection aims to find a small subset of predictors, so that the resulting linear model is expected to have the most desirable prediction accuracy. It is not only important and imperative in regression analysis but also has far-reaching applications in every facet of research, including computer science and medicine. We introduce a polynomial algorithm, which, under mild conditions, solves the problem. This algorithm exploits the idea of sequencing and splicing to reach a stable solu ...[more]

PMID: 33328272

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Project description:With evidence-based measures, COVID-19 can be effectively controlled by advanced data analysis and prediction. However, while valuable insights are available, there is a shortage of robust and rigorous research on what factors shape COVID-19 transmissions at the city cluster level. Therefore, to bridge the research gap, we adopted a data-driven hierarchical modeling approach to identify the most influential factors in shaping COVID-19 transmissions across different Chinese cities and clusters. The data used in this study are from Chinese officials, and hierarchical modeling conclusions drawn from the analysis are systematic, multifaceted, and comprehensive. To further improve research rigor, the study utilizes SPSS, Python and RStudio to conduct multiple linear regression and polynomial best subset regression (PBSR) analysis for the hierarchical modeling. The regression model utilizes the magnitude of various relative factors in nine Chinese city clusters, including 45 cities at a different level of clusters, to examine these aspects from the city cluster scale, exploring the correlation between various factors of the cities. These initial 12 factors are comprised of 'Urban population ratio', 'Retail sales of consumer goods', 'Number of tourists', 'Tourism Income', 'Ratio of the elderly population (> 60 year old) in this city', 'population density', 'Mobility scale (move in/inbound) during the spring festival', 'Ratio of Population and Health facilities', 'Jobless rate (%)', 'The straight-line distance from original epicenter Wuhan to this city', 'urban per capita GDP', and 'the prevalence of the COVID-19'. The study's results provide rigorously-tested and evidence-based insights on most instrumental factors that shape COVID-19 transmissions across cities and regions in China. Overall, the study findings found that per capita GDP and population mobility rates were the most affected factors in the prevalence of COVID-19 in a city, which could inform health experts and government officials to design and develop evidence-based and effective public health policies that could curb the spread of the COVID-19 pandemic.

Dataset Information

A polynomial algorithm for best-subset selection problem.

Publications

A polynomial algorithm for best-subset selection problem.

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