Estimates on learning rates for multi-penalty distribution regression

This paper is concerned with functional learning by utilizing two-stage sampled distribution regression. We study a multi-penalty regularization algorithm for distribution regression in the framework of learning theory. The algorithm aims at regressing to real-valued outputs from probability measures. The theoretical analysis of distribution regression is far from maturity and quite challenging since only second-stage samples are observable in practical settings. In our algorithm, to transform information of distribution samples, we embed the distributions to a reproducing kernel Hilbert space H K associated with Mercer kernel K via mean embedding technique. One of the primary contributions of this work is the introduction of a novel multi-penalty regularization algorithm, which is able to capture more potential features of distribution regression. Optimal learning rates of the algorithm are obtained under mild conditions. The work also derives learning rates for distribution regression in the hard learning scenario f ρ ∉ H K , which has not been explored in the existing literature. Moreover, we propose a new distribution-regression-based distributed learning algorithm to face large-scale data or information challenges arising from distribution data. The optimal learning rates are derived for the distributed learning algorithm. By providing new algorithms and showing their learning rates, the work improves the existing literature in various aspects. Ausführliche Beschreibung

Gespeichert in:

Autor*in:	Yu, Zhan [verfasserIn] Ho, Daniel W.C. [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2023

Schlagwörter:	Learning theory Distribution regression Distributed learning Integral operator Multi-penalty regularization Learning rate

Übergeordnetes Werk:	Enthalten in: Applied and computational harmonic analysis - San Diego, Calif. [u.a.] : Academic Pr., Elsevier Science, 1993, 69
Übergeordnetes Werk:	volume:69

DOI / URN:	10.1016/j.acha.2023.101609

Katalog-ID:	ELV066403693

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520			\|a This paper is concerned with functional learning by utilizing two-stage sampled distribution regression. We study a multi-penalty regularization algorithm for distribution regression in the framework of learning theory. The algorithm aims at regressing to real-valued outputs from probability measures. The theoretical analysis of distribution regression is far from maturity and quite challenging since only second-stage samples are observable in practical settings. In our algorithm, to transform information of distribution samples, we embed the distributions to a reproducing kernel Hilbert space H K associated with Mercer kernel K via mean embedding technique. One of the primary contributions of this work is the introduction of a novel multi-penalty regularization algorithm, which is able to capture more potential features of distribution regression. Optimal learning rates of the algorithm are obtained under mild conditions. The work also derives learning rates for distribution regression in the hard learning scenario f ρ ∉ H K , which has not been explored in the existing literature. Moreover, we propose a new distribution-regression-based distributed learning algorithm to face large-scale data or information challenges arising from distribution data. The optimal learning rates are derived for the distributed learning algorithm. By providing new algorithms and showing their learning rates, the work improves the existing literature in various aspects.
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allfields	10.1016/j.acha.2023.101609 doi (DE-627)ELV066403693 (ELSEVIER)S1063-5203(23)00096-9 DE-627 ger DE-627 rda eng 510 VZ 31.35 bkl Yu, Zhan verfasserin (orcid)0000-0002-2194-0101 aut Estimates on learning rates for multi-penalty distribution regression 2023 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier This paper is concerned with functional learning by utilizing two-stage sampled distribution regression. We study a multi-penalty regularization algorithm for distribution regression in the framework of learning theory. The algorithm aims at regressing to real-valued outputs from probability measures. The theoretical analysis of distribution regression is far from maturity and quite challenging since only second-stage samples are observable in practical settings. In our algorithm, to transform information of distribution samples, we embed the distributions to a reproducing kernel Hilbert space H K associated with Mercer kernel K via mean embedding technique. One of the primary contributions of this work is the introduction of a novel multi-penalty regularization algorithm, which is able to capture more potential features of distribution regression. Optimal learning rates of the algorithm are obtained under mild conditions. The work also derives learning rates for distribution regression in the hard learning scenario f ρ ∉ H K , which has not been explored in the existing literature. Moreover, we propose a new distribution-regression-based distributed learning algorithm to face large-scale data or information challenges arising from distribution data. The optimal learning rates are derived for the distributed learning algorithm. By providing new algorithms and showing their learning rates, the work improves the existing literature in various aspects. Learning theory Distribution regression Distributed learning Integral operator Multi-penalty regularization Learning rate Ho, Daniel W.C. verfasserin aut Enthalten in Applied and computational harmonic analysis San Diego, Calif. [u.a.] : Academic Pr., Elsevier Science, 1993 69 Online-Ressource (DE-627)254231314 (DE-600)1461358-X (DE-576)103373012 1096-603X nnns volume:69 GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OPC-MAT GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2014 GBV_ILN_2025 GBV_ILN_2034 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2056 GBV_ILN_2064 GBV_ILN_2088 GBV_ILN_2106 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2122 GBV_ILN_2143 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 31.35 Harmonische Analyse VZ AR 69
spelling	10.1016/j.acha.2023.101609 doi (DE-627)ELV066403693 (ELSEVIER)S1063-5203(23)00096-9 DE-627 ger DE-627 rda eng 510 VZ 31.35 bkl Yu, Zhan verfasserin (orcid)0000-0002-2194-0101 aut Estimates on learning rates for multi-penalty distribution regression 2023 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier This paper is concerned with functional learning by utilizing two-stage sampled distribution regression. We study a multi-penalty regularization algorithm for distribution regression in the framework of learning theory. The algorithm aims at regressing to real-valued outputs from probability measures. The theoretical analysis of distribution regression is far from maturity and quite challenging since only second-stage samples are observable in practical settings. In our algorithm, to transform information of distribution samples, we embed the distributions to a reproducing kernel Hilbert space H K associated with Mercer kernel K via mean embedding technique. One of the primary contributions of this work is the introduction of a novel multi-penalty regularization algorithm, which is able to capture more potential features of distribution regression. Optimal learning rates of the algorithm are obtained under mild conditions. The work also derives learning rates for distribution regression in the hard learning scenario f ρ ∉ H K , which has not been explored in the existing literature. Moreover, we propose a new distribution-regression-based distributed learning algorithm to face large-scale data or information challenges arising from distribution data. The optimal learning rates are derived for the distributed learning algorithm. By providing new algorithms and showing their learning rates, the work improves the existing literature in various aspects. Learning theory Distribution regression Distributed learning Integral operator Multi-penalty regularization Learning rate Ho, Daniel W.C. verfasserin aut Enthalten in Applied and computational harmonic analysis San Diego, Calif. [u.a.] : Academic Pr., Elsevier Science, 1993 69 Online-Ressource (DE-627)254231314 (DE-600)1461358-X (DE-576)103373012 1096-603X nnns volume:69 GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OPC-MAT GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2014 GBV_ILN_2025 GBV_ILN_2034 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2056 GBV_ILN_2064 GBV_ILN_2088 GBV_ILN_2106 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2122 GBV_ILN_2143 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 31.35 Harmonische Analyse VZ AR 69
allfields_unstemmed	10.1016/j.acha.2023.101609 doi (DE-627)ELV066403693 (ELSEVIER)S1063-5203(23)00096-9 DE-627 ger DE-627 rda eng 510 VZ 31.35 bkl Yu, Zhan verfasserin (orcid)0000-0002-2194-0101 aut Estimates on learning rates for multi-penalty distribution regression 2023 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier This paper is concerned with functional learning by utilizing two-stage sampled distribution regression. We study a multi-penalty regularization algorithm for distribution regression in the framework of learning theory. The algorithm aims at regressing to real-valued outputs from probability measures. The theoretical analysis of distribution regression is far from maturity and quite challenging since only second-stage samples are observable in practical settings. In our algorithm, to transform information of distribution samples, we embed the distributions to a reproducing kernel Hilbert space H K associated with Mercer kernel K via mean embedding technique. One of the primary contributions of this work is the introduction of a novel multi-penalty regularization algorithm, which is able to capture more potential features of distribution regression. Optimal learning rates of the algorithm are obtained under mild conditions. The work also derives learning rates for distribution regression in the hard learning scenario f ρ ∉ H K , which has not been explored in the existing literature. Moreover, we propose a new distribution-regression-based distributed learning algorithm to face large-scale data or information challenges arising from distribution data. The optimal learning rates are derived for the distributed learning algorithm. By providing new algorithms and showing their learning rates, the work improves the existing literature in various aspects. Learning theory Distribution regression Distributed learning Integral operator Multi-penalty regularization Learning rate Ho, Daniel W.C. verfasserin aut Enthalten in Applied and computational harmonic analysis San Diego, Calif. [u.a.] : Academic Pr., Elsevier Science, 1993 69 Online-Ressource (DE-627)254231314 (DE-600)1461358-X (DE-576)103373012 1096-603X nnns volume:69 GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OPC-MAT GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2014 GBV_ILN_2025 GBV_ILN_2034 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2056 GBV_ILN_2064 GBV_ILN_2088 GBV_ILN_2106 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2122 GBV_ILN_2143 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 31.35 Harmonische Analyse VZ AR 69
allfieldsGer	10.1016/j.acha.2023.101609 doi (DE-627)ELV066403693 (ELSEVIER)S1063-5203(23)00096-9 DE-627 ger DE-627 rda eng 510 VZ 31.35 bkl Yu, Zhan verfasserin (orcid)0000-0002-2194-0101 aut Estimates on learning rates for multi-penalty distribution regression 2023 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier This paper is concerned with functional learning by utilizing two-stage sampled distribution regression. We study a multi-penalty regularization algorithm for distribution regression in the framework of learning theory. The algorithm aims at regressing to real-valued outputs from probability measures. The theoretical analysis of distribution regression is far from maturity and quite challenging since only second-stage samples are observable in practical settings. In our algorithm, to transform information of distribution samples, we embed the distributions to a reproducing kernel Hilbert space H K associated with Mercer kernel K via mean embedding technique. One of the primary contributions of this work is the introduction of a novel multi-penalty regularization algorithm, which is able to capture more potential features of distribution regression. Optimal learning rates of the algorithm are obtained under mild conditions. The work also derives learning rates for distribution regression in the hard learning scenario f ρ ∉ H K , which has not been explored in the existing literature. Moreover, we propose a new distribution-regression-based distributed learning algorithm to face large-scale data or information challenges arising from distribution data. The optimal learning rates are derived for the distributed learning algorithm. By providing new algorithms and showing their learning rates, the work improves the existing literature in various aspects. Learning theory Distribution regression Distributed learning Integral operator Multi-penalty regularization Learning rate Ho, Daniel W.C. verfasserin aut Enthalten in Applied and computational harmonic analysis San Diego, Calif. [u.a.] : Academic Pr., Elsevier Science, 1993 69 Online-Ressource (DE-627)254231314 (DE-600)1461358-X (DE-576)103373012 1096-603X nnns volume:69 GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OPC-MAT GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2014 GBV_ILN_2025 GBV_ILN_2034 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2056 GBV_ILN_2064 GBV_ILN_2088 GBV_ILN_2106 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2122 GBV_ILN_2143 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 31.35 Harmonische Analyse VZ AR 69
allfieldsSound	10.1016/j.acha.2023.101609 doi (DE-627)ELV066403693 (ELSEVIER)S1063-5203(23)00096-9 DE-627 ger DE-627 rda eng 510 VZ 31.35 bkl Yu, Zhan verfasserin (orcid)0000-0002-2194-0101 aut Estimates on learning rates for multi-penalty distribution regression 2023 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier This paper is concerned with functional learning by utilizing two-stage sampled distribution regression. We study a multi-penalty regularization algorithm for distribution regression in the framework of learning theory. The algorithm aims at regressing to real-valued outputs from probability measures. The theoretical analysis of distribution regression is far from maturity and quite challenging since only second-stage samples are observable in practical settings. In our algorithm, to transform information of distribution samples, we embed the distributions to a reproducing kernel Hilbert space H K associated with Mercer kernel K via mean embedding technique. One of the primary contributions of this work is the introduction of a novel multi-penalty regularization algorithm, which is able to capture more potential features of distribution regression. Optimal learning rates of the algorithm are obtained under mild conditions. The work also derives learning rates for distribution regression in the hard learning scenario f ρ ∉ H K , which has not been explored in the existing literature. Moreover, we propose a new distribution-regression-based distributed learning algorithm to face large-scale data or information challenges arising from distribution data. The optimal learning rates are derived for the distributed learning algorithm. By providing new algorithms and showing their learning rates, the work improves the existing literature in various aspects. Learning theory Distribution regression Distributed learning Integral operator Multi-penalty regularization Learning rate Ho, Daniel W.C. verfasserin aut Enthalten in Applied and computational harmonic analysis San Diego, Calif. [u.a.] : Academic Pr., Elsevier Science, 1993 69 Online-Ressource (DE-627)254231314 (DE-600)1461358-X (DE-576)103373012 1096-603X nnns volume:69 GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OPC-MAT GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2014 GBV_ILN_2025 GBV_ILN_2034 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2056 GBV_ILN_2064 GBV_ILN_2088 GBV_ILN_2106 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2122 GBV_ILN_2143 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 31.35 Harmonische Analyse VZ AR 69
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author	Yu, Zhan
spellingShingle	Yu, Zhan ddc 510 bkl 31.35 misc Learning theory misc Distribution regression misc Distributed learning misc Integral operator misc Multi-penalty regularization misc Learning rate Estimates on learning rates for multi-penalty distribution regression
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topic_title	510 VZ 31.35 bkl Estimates on learning rates for multi-penalty distribution regression Learning theory Distribution regression Distributed learning Integral operator Multi-penalty regularization Learning rate
topic	ddc 510 bkl 31.35 misc Learning theory misc Distribution regression misc Distributed learning misc Integral operator misc Multi-penalty regularization misc Learning rate
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title	Estimates on learning rates for multi-penalty distribution regression
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title_sort	estimates on learning rates for multi-penalty distribution regression
title_auth	Estimates on learning rates for multi-penalty distribution regression
abstract	This paper is concerned with functional learning by utilizing two-stage sampled distribution regression. We study a multi-penalty regularization algorithm for distribution regression in the framework of learning theory. The algorithm aims at regressing to real-valued outputs from probability measures. The theoretical analysis of distribution regression is far from maturity and quite challenging since only second-stage samples are observable in practical settings. In our algorithm, to transform information of distribution samples, we embed the distributions to a reproducing kernel Hilbert space H K associated with Mercer kernel K via mean embedding technique. One of the primary contributions of this work is the introduction of a novel multi-penalty regularization algorithm, which is able to capture more potential features of distribution regression. Optimal learning rates of the algorithm are obtained under mild conditions. The work also derives learning rates for distribution regression in the hard learning scenario f ρ ∉ H K , which has not been explored in the existing literature. Moreover, we propose a new distribution-regression-based distributed learning algorithm to face large-scale data or information challenges arising from distribution data. The optimal learning rates are derived for the distributed learning algorithm. By providing new algorithms and showing their learning rates, the work improves the existing literature in various aspects.
abstractGer	This paper is concerned with functional learning by utilizing two-stage sampled distribution regression. We study a multi-penalty regularization algorithm for distribution regression in the framework of learning theory. The algorithm aims at regressing to real-valued outputs from probability measures. The theoretical analysis of distribution regression is far from maturity and quite challenging since only second-stage samples are observable in practical settings. In our algorithm, to transform information of distribution samples, we embed the distributions to a reproducing kernel Hilbert space H K associated with Mercer kernel K via mean embedding technique. One of the primary contributions of this work is the introduction of a novel multi-penalty regularization algorithm, which is able to capture more potential features of distribution regression. Optimal learning rates of the algorithm are obtained under mild conditions. The work also derives learning rates for distribution regression in the hard learning scenario f ρ ∉ H K , which has not been explored in the existing literature. Moreover, we propose a new distribution-regression-based distributed learning algorithm to face large-scale data or information challenges arising from distribution data. The optimal learning rates are derived for the distributed learning algorithm. By providing new algorithms and showing their learning rates, the work improves the existing literature in various aspects.
abstract_unstemmed	This paper is concerned with functional learning by utilizing two-stage sampled distribution regression. We study a multi-penalty regularization algorithm for distribution regression in the framework of learning theory. The algorithm aims at regressing to real-valued outputs from probability measures. The theoretical analysis of distribution regression is far from maturity and quite challenging since only second-stage samples are observable in practical settings. In our algorithm, to transform information of distribution samples, we embed the distributions to a reproducing kernel Hilbert space H K associated with Mercer kernel K via mean embedding technique. One of the primary contributions of this work is the introduction of a novel multi-penalty regularization algorithm, which is able to capture more potential features of distribution regression. Optimal learning rates of the algorithm are obtained under mild conditions. The work also derives learning rates for distribution regression in the hard learning scenario f ρ ∉ H K , which has not been explored in the existing literature. Moreover, we propose a new distribution-regression-based distributed learning algorithm to face large-scale data or information challenges arising from distribution data. The optimal learning rates are derived for the distributed learning algorithm. By providing new algorithms and showing their learning rates, the work improves the existing literature in various aspects.
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title_short	Estimates on learning rates for multi-penalty distribution regression
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doi_str	10.1016/j.acha.2023.101609
up_date	2024-07-06T17:38:12.593Z
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Moreover, we propose a new distribution-regression-based distributed learning algorithm to face large-scale data or information challenges arising from distribution data. The optimal learning rates are derived for the distributed learning algorithm. 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Estimates on learning rates for multi-penalty distribution regression

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