Please use this identifier to cite or link to this item:
http://hdl.handle.net/10397/106818
DC Field | Value | Language |
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dc.contributor | Department of Applied Mathematics | - |
dc.creator | Shen, G | - |
dc.creator | Jiao, Y | - |
dc.creator | Lin, Y | - |
dc.creator | Horowitz, JL | - |
dc.creator | Huang, J | - |
dc.date.accessioned | 2024-06-04T07:39:57Z | - |
dc.date.available | 2024-06-04T07:39:57Z | - |
dc.identifier.issn | 1532-4435 | - |
dc.identifier.uri | http://hdl.handle.net/10397/106818 | - |
dc.language.iso | en | en_US |
dc.publisher | Journal of Machine Learning Research | en_US |
dc.rights | © 2024 Guohao Shen, Yuling Jiao, Yuanyuan Lin, Joel Horowitz and Jian Huang. | en_US |
dc.rights | License: CC-BY 4.0, see https://creativecommons.org/licenses/by/4.0/. Attribution requirements are provided at http://jmlr.org/papers/v25/22-0488.html. | en_US |
dc.rights | The following publication Guohao Shen; Yuling Jiao; Yuanyuan Lin; Joel L. Horowitz; Jian Huang (2024). Nonparametric Estimation of Non-Crossing Quantile Regression Process with Deep ReQU Neural Networks. Journal of Machine Learning Research, 25(88), 1-75 is available at https://www.jmlr.org/papers/v25/22-0488.html. | en_US |
dc.subject | Approximation error | en_US |
dc.subject | Deep neural networks | en_US |
dc.subject | Monotonic constraints | en_US |
dc.subject | Non-asymptotic error bound | en_US |
dc.subject | Quantile process | en_US |
dc.title | Nonparametric estimation of non-crossing quantile regression process with deep ReQU neural networks | en_US |
dc.type | Journal/Magazine Article | en_US |
dc.identifier.spage | 1 | - |
dc.identifier.epage | 75 | - |
dc.identifier.volume | 25 | - |
dc.identifier.issue | 88 | - |
dcterms.abstract | We propose a penalized nonparametric approach to estimating the quantile regression process (QRP) in a nonseparable model using rectifier quadratic unit (ReQU) activated deep neural networks and introduce a novel penalty function to enforce non-crossing of quantile regression curves. We establish the non-asymptotic excess risk bounds for the estimated QRP and derive the mean integrated squared error for the estimated QRP under mild smoothness and regularity conditions. To establish these non-asymptotic risk and estimation error bounds, we also develop a new error bound for approximating Cs smooth functions with s > 1 and their derivatives using ReQU activated neural networks. This is a new approximation result for ReQU networks and is of independent interest and may be useful in other problems. Our numerical experiments demonstrate that the proposed method is competitive with or outperforms two existing methods, including methods using reproducing kernels and random forests for nonparametric quantile regression. | - |
dcterms.accessRights | open access | en_US |
dcterms.bibliographicCitation | Journal of machine learning research, 2024, v. 25, no. 88, p. 1-75 | - |
dcterms.isPartOf | Journal of machine learning research | - |
dcterms.issued | 2024 | - |
dc.identifier.eissn | 1533-7928 | - |
dc.description.validate | 202406 bcch | - |
dc.description.oa | Version of Record | en_US |
dc.identifier.FolderNumber | a2752 | en_US |
dc.identifier.SubFormID | 48236 | en_US |
dc.description.fundingSource | RGC | en_US |
dc.description.fundingSource | Others | en_US |
dc.description.fundingText | G. Shen is partially supported by the Hong Kong Research Grants Council (Grant No. 15305523) and a research grant from The Hong Kong Polytechnic University. The work of Y. Jiao is supported by the National Nature Science Foundation of China (Grant No.12371441), “the Fundamental Research Funds for the Central Universities”, and the research fund of KLATASDSMOE of China. Y. Lin’s research was partially supported by the Hong Kong Research Grants Council (Grant No. 14306219, 14306620, 14304523), and Direct Grants for Research, The Chinese University of Hong Kong. The work of J. Huang is supported by the National Natural Science Foundation of China (Grant No. 72331005) and research grants from The Hong Kong Polytechnic University. | en_US |
dc.description.pubStatus | Published | en_US |
dc.description.oaCategory | CC | en_US |
Appears in Collections: | Journal/Magazine Article |
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22-0488.pdf | 6.85 MB | Adobe PDF | View/Open |
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