On Quantile Regression in Reproducing Kernel Hilbert Spaces with Data Sparsity Constraint.

IF 4.3 3区 计算机科学 Q1 AUTOMATION & CONTROL SYSTEMS
Journal of Machine Learning Research Pub Date : 2016-04-01
Chong Zhang, Yufeng Liu, Yichao Wu
{"title":"On Quantile Regression in Reproducing Kernel Hilbert Spaces with Data Sparsity Constraint.","authors":"Chong Zhang,&nbsp;Yufeng Liu,&nbsp;Yichao Wu","doi":"","DOIUrl":null,"url":null,"abstract":"<p><p>For spline regressions, it is well known that the choice of knots is crucial for the performance of the estimator. As a general learning framework covering the smoothing splines, learning in a Reproducing Kernel Hilbert Space (RKHS) has a similar issue. However, the selection of training data points for kernel functions in the RKHS representation has not been carefully studied in the literature. In this paper we study quantile regression as an example of learning in a RKHS. In this case, the regular squared norm penalty does not perform training data selection. We propose a data sparsity constraint that imposes thresholding on the kernel function coefficients to achieve a sparse kernel function representation. We demonstrate that the proposed data sparsity method can have competitive prediction performance for certain situations, and have comparable performance in other cases compared to that of the traditional squared norm penalty. Therefore, the data sparsity method can serve as a competitive alternative to the squared norm penalty method. Some theoretical properties of our proposed method using the data sparsity constraint are obtained. Both simulated and real data sets are used to demonstrate the usefulness of our data sparsity constraint.</p>","PeriodicalId":50161,"journal":{"name":"Journal of Machine Learning Research","volume":null,"pages":null},"PeriodicalIF":4.3000,"publicationDate":"2016-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4850041/pdf/nihms729829.pdf","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Machine Learning Research","FirstCategoryId":"94","ListUrlMain":"","RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"AUTOMATION & CONTROL SYSTEMS","Score":null,"Total":0}
引用次数: 0

Abstract

For spline regressions, it is well known that the choice of knots is crucial for the performance of the estimator. As a general learning framework covering the smoothing splines, learning in a Reproducing Kernel Hilbert Space (RKHS) has a similar issue. However, the selection of training data points for kernel functions in the RKHS representation has not been carefully studied in the literature. In this paper we study quantile regression as an example of learning in a RKHS. In this case, the regular squared norm penalty does not perform training data selection. We propose a data sparsity constraint that imposes thresholding on the kernel function coefficients to achieve a sparse kernel function representation. We demonstrate that the proposed data sparsity method can have competitive prediction performance for certain situations, and have comparable performance in other cases compared to that of the traditional squared norm penalty. Therefore, the data sparsity method can serve as a competitive alternative to the squared norm penalty method. Some theoretical properties of our proposed method using the data sparsity constraint are obtained. Both simulated and real data sets are used to demonstrate the usefulness of our data sparsity constraint.

Abstract Image

Abstract Image

数据稀疏性约束下核希尔伯特空间再现的分位数回归。
对于样条回归,众所周知,结点的选择对估计器的性能至关重要。作为覆盖光滑样条的一般学习框架,在再现核希尔伯特空间(RKHS)中学习也存在类似的问题。然而,在RKHS表示中,核函数的训练数据点的选择并没有在文献中得到仔细的研究。本文研究了分位数回归作为RKHS学习的一个例子。在这种情况下,正则平方范数惩罚不执行训练数据选择。我们提出了一种数据稀疏性约束,对核函数系数施加阈值以实现稀疏核函数表示。我们证明了所提出的数据稀疏性方法在某些情况下可以具有竞争性的预测性能,并且在其他情况下与传统的平方范数惩罚相比具有可比的性能。因此,数据稀疏性方法可以作为平方范数惩罚方法的竞争性替代方法。给出了该方法在数据稀疏性约束下的一些理论性质。模拟数据集和真实数据集都被用来证明我们的数据稀疏性约束的有效性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 求助全文
来源期刊
Journal of Machine Learning Research
Journal of Machine Learning Research 工程技术-计算机:人工智能
CiteScore
18.80
自引率
0.00%
发文量
2
审稿时长
3 months
期刊介绍: The Journal of Machine Learning Research (JMLR) provides an international forum for the electronic and paper publication of high-quality scholarly articles in all areas of machine learning. All published papers are freely available online. JMLR has a commitment to rigorous yet rapid reviewing. JMLR seeks previously unpublished papers on machine learning that contain: new principled algorithms with sound empirical validation, and with justification of theoretical, psychological, or biological nature; experimental and/or theoretical studies yielding new insight into the design and behavior of learning in intelligent systems; accounts of applications of existing techniques that shed light on the strengths and weaknesses of the methods; formalization of new learning tasks (e.g., in the context of new applications) and of methods for assessing performance on those tasks; development of new analytical frameworks that advance theoretical studies of practical learning methods; computational models of data from natural learning systems at the behavioral or neural level; or extremely well-written surveys of existing work.
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信