{"title":"Variable selection using axis-aligned random projections for partial least-squares regression","authors":"","doi":"10.1007/s11222-024-10417-5","DOIUrl":null,"url":null,"abstract":"<h3>Abstract</h3> <p>In high-dimensional data modeling, variable selection plays a crucial role in improving predictive accuracy and enhancing model interpretability through sparse representation. Unfortunately, certain variable selection methods encounter challenges such as insufficient model sparsity, high computational overhead, and difficulties in handling large-scale data. Recently, axis-aligned random projection techniques have been applied to address these issues by selecting variables. However, these techniques have seen limited application in handling complex data within the regression framework. In this study, we propose a novel method, sparse partial least squares via axis-aligned random projection, designed for the analysis of high-dimensional data. Initially, axis-aligned random projection is utilized to obtain a sparse loading vector, significantly reducing computational complexity. Subsequently, partial least squares regression is conducted within the subspace of the top-ranked significant variables. The submatrices are iteratively updated until an optimal sparse partial least squares model is achieved. Comparative analysis with some state-of-the-art high-dimensional regression methods demonstrates that the proposed method exhibits superior predictive performance. To illustrate its effectiveness, we apply the method to four cases, including one simulated dataset and three real-world datasets. The results show the proposed method’s ability to identify important variables in all four cases.</p>","PeriodicalId":22058,"journal":{"name":"Statistics and Computing","volume":"39 1","pages":""},"PeriodicalIF":1.6000,"publicationDate":"2024-03-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Statistics and Computing","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s11222-024-10417-5","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"COMPUTER SCIENCE, THEORY & METHODS","Score":null,"Total":0}
引用次数: 0
Abstract
In high-dimensional data modeling, variable selection plays a crucial role in improving predictive accuracy and enhancing model interpretability through sparse representation. Unfortunately, certain variable selection methods encounter challenges such as insufficient model sparsity, high computational overhead, and difficulties in handling large-scale data. Recently, axis-aligned random projection techniques have been applied to address these issues by selecting variables. However, these techniques have seen limited application in handling complex data within the regression framework. In this study, we propose a novel method, sparse partial least squares via axis-aligned random projection, designed for the analysis of high-dimensional data. Initially, axis-aligned random projection is utilized to obtain a sparse loading vector, significantly reducing computational complexity. Subsequently, partial least squares regression is conducted within the subspace of the top-ranked significant variables. The submatrices are iteratively updated until an optimal sparse partial least squares model is achieved. Comparative analysis with some state-of-the-art high-dimensional regression methods demonstrates that the proposed method exhibits superior predictive performance. To illustrate its effectiveness, we apply the method to four cases, including one simulated dataset and three real-world datasets. The results show the proposed method’s ability to identify important variables in all four cases.
期刊介绍：
Statistics and Computing is a bi-monthly refereed journal which publishes papers covering the range of the interface between the statistical and computing sciences.
In particular, it addresses the use of statistical concepts in computing science, for example in machine learning, computer vision and data analytics, as well as the use of computers in data modelling, prediction and analysis. Specific topics which are covered include: techniques for evaluating analytically intractable problems such as bootstrap resampling, Markov chain Monte Carlo, sequential Monte Carlo, approximate Bayesian computation, search and optimization methods, stochastic simulation and Monte Carlo, graphics, computer environments, statistical approaches to software errors, information retrieval, machine learning, statistics of databases and database technology, huge data sets and big data analytics, computer algebra, graphical models, image processing, tomography, inverse problems and uncertainty quantification.
In addition, the journal contains original research reports, authoritative review papers, discussed papers, and occasional special issues on particular topics or carrying proceedings of relevant conferences. Statistics and Computing also publishes book review and software review sections.
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