Variable transformations in combination with wavelets and ANOVA for high-dimensional approximation
We use hyperbolic wavelet regression for the fast reconstruction of high-dimensional functions having only low-dimensional variable interactions. Compactly supported periodic Chui-Wang wavelets are used for the tensorized hyperbolic wavelet basis on the torus. With a variable transformation, we are...
Uložené v:
| Vydané v: | Advances in computational mathematics Ročník 50; číslo 3; s. 53 |
|---|---|
| Hlavní autori: | , |
| Médium: | Journal Article |
| Jazyk: | English |
| Vydavateľské údaje: |
New York
Springer US
01.06.2024
Springer Nature B.V |
| Predmet: | |
| ISSN: | 1019-7168, 1572-9044 |
| On-line prístup: | Získať plný text |
| Tagy: |
Pridať tag
Žiadne tagy, Buďte prvý, kto otaguje tento záznam!
|
| Abstract | We use hyperbolic wavelet regression for the fast reconstruction of high-dimensional functions having only low-dimensional variable interactions. Compactly supported periodic Chui-Wang wavelets are used for the tensorized hyperbolic wavelet basis on the torus. With a variable transformation, we are able to transform the approximation rates and fast algorithms from the torus to other domains. We perform and analyze scattered data approximation for smooth but arbitrary density functions by using a least squares method. The corresponding system matrix is sparse due to the compact support of the wavelets, which leads to a significant acceleration of the matrix vector multiplication. For non-periodic functions, we propose a new extension method. A proper choice of the extension parameter together with the piecewise polynomial Chui-Wang wavelets extends the functions appropriately. In every case, we are able to bound the approximation error with high probability. Additionally, if the function has a low effective dimension (i.e., only interactions of a few variables), we qualitatively determine the variable interactions and omit ANOVA terms with low variance in a second step in order to decrease the approximation error. This allows us to suggest an adapted model for the approximation. Numerical results show the efficiency of the proposed method. |
|---|---|
| AbstractList | We use hyperbolic wavelet regression for the fast reconstruction of high-dimensional functions having only low-dimensional variable interactions. Compactly supported periodic Chui-Wang wavelets are used for the tensorized hyperbolic wavelet basis on the torus. With a variable transformation, we are able to transform the approximation rates and fast algorithms from the torus to other domains. We perform and analyze scattered data approximation for smooth but arbitrary density functions by using a least squares method. The corresponding system matrix is sparse due to the compact support of the wavelets, which leads to a significant acceleration of the matrix vector multiplication. For non-periodic functions, we propose a new extension method. A proper choice of the extension parameter together with the piecewise polynomial Chui-Wang wavelets extends the functions appropriately. In every case, we are able to bound the approximation error with high probability. Additionally, if the function has a low effective dimension (i.e., only interactions of a few variables), we qualitatively determine the variable interactions and omit ANOVA terms with low variance in a second step in order to decrease the approximation error. This allows us to suggest an adapted model for the approximation. Numerical results show the efficiency of the proposed method. |
| ArticleNumber | 53 |
| Author | Potts, Daniel Weidensager, Laura |
| Author_xml | – sequence: 1 givenname: Daniel orcidid: 0000-0003-3651-4364 surname: Potts fullname: Potts, Daniel organization: Faculty of Mathematics, Chemnitz University of Technology – sequence: 2 givenname: Laura orcidid: 0000-0001-7988-1485 surname: Weidensager fullname: Weidensager, Laura email: laura.weidensager@math.tu-chemnitz.de organization: Faculty of Mathematics, Chemnitz University of Technology |
| BookMark | eNp9kEtLAzEUhYNU0Kp_wFXAdTTvmVkW8QXFbrTbkMkkbco0U5Op1X9v2hEEF13dXHK-e889YzAKXbAAXBN8SzAu7hLBnHOEKUcEE14gegLOiSgoqvLHKL8xqVBBZHkGximtMMaVLMQ5qOc6el23FvZRh-S6uNa970KCPkDTrWsfDj3c-X4Jd_rTtrZPUIcGTl5n8wnMBFz6xRI1fm1DylLdQr3ZxO7LD6MuwanTbbJXv_UCvD8-vN0_o-ns6eV-MkWGSdajxhknmRGWSU2Ztk5a63iBjaCOikZUpGa0wtpRWxa2wbYk3NQcl1jkS7RkF-BmmJt3f2xt6tWq28ZsJylGBadUyIpmFR1UJnYpRevUJmaj8VsRrPZZqiFLlbNUhyzVHir_Qcb3h-Nyar49jrIBTXlPWNj45-oI9QM7Dowj |
| CitedBy_id | crossref_primary_10_1109_JSTARS_2025_3529704 |
| Cites_doi | 10.1137/17M1114697 10.2307/1968431 10.1006/acha.1998.0247 10.1016/j.jco.2013.07.001 10.1090/S0025-5718-09-02319-9 10.1137/20M1354921 10.1017/fms.2020.23 10.1090/S0025-5718-2014-02883-4 10.1016/j.acha.2022.08.003 10.1198/106186007X237892 10.1007/s10444-008-9064-9 10.1016/j.jco.2021.101602 10.1007/978-3-319-71688-6 10.1007/978-1-4899-4493-1 10.1007/s43670-023-00063-9 10.5802/smai-jcm.24 10.1137/090752456 10.21314/JCF.1997.005 10.1007/s10208-013-9142-3 10.4171/026 10.1007/s00211-023-01358-8 10.1016/S0378-4754(00)00270-6 10.1016/j.jco.2010.04.003 10.1007/978-3-642-16004-2 10.1007/s12283-023-00444-2 10.1090/mcom/3718 10.1007/s00365-021-09555-0 10.1007/978-3-319-92240-9 10.3389/fams.2022.795250 10.1137/21M1407707 10.1016/j.camwa.2010.10.015 10.1137/1.9781611976885 10.1007/s00365-010-9105-8 10.1198/016214505000001410 10.1111/j.2517-6161.1991.tb01857.x 10.1090/mcom/3754 |
| ContentType | Journal Article |
| Copyright | The Author(s) 2024 The Author(s) 2024. This work is published under http://creativecommons.org/licenses/by/4.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License. |
| Copyright_xml | – notice: The Author(s) 2024 – notice: The Author(s) 2024. This work is published under http://creativecommons.org/licenses/by/4.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License. |
| DBID | C6C AAYXX CITATION 8FE 8FG ABJCF AFKRA ARAPS AZQEC BENPR BGLVJ CCPQU DWQXO GNUQQ HCIFZ JQ2 K7- L6V M7S P5Z P62 PHGZM PHGZT PKEHL PQEST PQGLB PQQKQ PQUKI PRINS PTHSS |
| DOI | 10.1007/s10444-024-10147-2 |
| DatabaseName | Springer Nature OA Free Journals CrossRef ProQuest SciTech Collection ProQuest Technology Collection Materials Science & Engineering Collection ProQuest Central UK/Ireland Advanced Technologies & Computer Science Collection ProQuest Central Essentials - QC ProQuest Central ProQuest Technology Collection ProQuest One ProQuest Central Korea ProQuest Central Student SciTech Premium Collection ProQuest Computer Science Collection Computer Science Database ProQuest Engineering Collection Engineering Database Advanced Technologies & Aerospace Database ProQuest Advanced Technologies & Aerospace Collection Proquest Central Premium ProQuest One Academic (New) ProQuest One Academic Middle East (New) ProQuest One Academic Eastern Edition (DO NOT USE) ProQuest One Applied & Life Sciences ProQuest One Academic (retired) ProQuest One Academic UKI Edition ProQuest Central China Engineering Collection |
| DatabaseTitle | CrossRef Computer Science Database ProQuest Central Student Technology Collection ProQuest One Academic Middle East (New) ProQuest Advanced Technologies & Aerospace Collection ProQuest Central Essentials ProQuest Computer Science Collection SciTech Premium Collection ProQuest One Community College ProQuest Central China ProQuest Central ProQuest One Applied & Life Sciences ProQuest Engineering Collection ProQuest Central Korea ProQuest Central (New) Engineering Collection Advanced Technologies & Aerospace Collection Engineering Database ProQuest One Academic Eastern Edition ProQuest Technology Collection ProQuest SciTech Collection Advanced Technologies & Aerospace Database ProQuest One Academic UKI Edition Materials Science & Engineering Collection ProQuest One Academic ProQuest One Academic (New) |
| DatabaseTitleList | CrossRef Computer Science Database |
| Database_xml | – sequence: 1 dbid: BENPR name: ProQuest Central url: https://www.proquest.com/central sourceTypes: Aggregation Database |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Applied Sciences Mathematics |
| EISSN | 1572-9044 |
| ExternalDocumentID | 10_1007_s10444_024_10147_2 |
| GrantInformation_xml | – fundername: Bundesministerium für Bildung und Forschung grantid: 01|S20053A funderid: http://dx.doi.org/10.13039/501100002347 – fundername: Deutsche Forschungsgemeinschaft grantid: CRC 1410; CRC 1410 funderid: http://dx.doi.org/10.13039/501100001659 |
| GroupedDBID | -52 -59 -5G -BR -EM -Y2 -~C .4S .86 .DC .VR 06D 0R~ 0VY 199 1N0 1SB 2.D 203 23M 28- 2J2 2JN 2JY 2KG 2KM 2LR 2P1 2VQ 2~H 30V 4.4 406 408 409 40D 40E 5GY 5QI 5VS 67Z 6NX 78A 8TC 8UJ 95- 95. 95~ 96X AAAVM AABHQ AACDK AAHNG AAIAL AAJBT AAJKR AANZL AARHV AARTL AASML AATNV AATVU AAUYE AAWCG AAYIU AAYQN AAYTO AAYZH ABAKF ABBBX ABBXA ABDZT ABECU ABFTV ABHLI ABHQN ABJNI ABJOX ABKCH ABKTR ABLJU ABMNI ABMQK ABNWP ABQBU ABQSL ABSXP ABTEG ABTHY ABTKH ABTMW ABULA ABWNU ABXPI ACAOD ACBXY ACDTI ACGFS ACHSB ACHXU ACIWK ACKNC ACMDZ ACMLO ACOKC ACOMO ACPIV ACSNA ACZOJ ADHHG ADHIR ADIMF ADINQ ADKNI ADKPE ADRFC ADTPH ADURQ ADYFF ADZKW AEBTG AEFIE AEFQL AEGAL AEGNC AEJHL AEJRE AEKMD AEMSY AENEX AEOHA AEPYU AESKC AETLH AEVLU AEXYK AFBBN AFEXP AFGCZ AFLOW AFQWF AFWTZ AFZKB AGAYW AGDGC AGGDS AGJBK AGMZJ AGQEE AGQMX AGRTI AGWIL AGWZB AGYKE AHAVH AHBYD AHKAY AHSBF AHYZX AIAKS AIGIU AIIXL AILAN AITGF AJBLW AJRNO AJZVZ ALMA_UNASSIGNED_HOLDINGS ALWAN AMKLP AMXSW AMYLF AMYQR AOCGG ARCSS ARMRJ ASPBG AVWKF AXYYD AYJHY AZFZN B-. BA0 BAPOH BBWZM BDATZ BGNMA BSONS C6C CAG COF CS3 CSCUP DDRTE DL5 DNIVK DPUIP EBLON EBS EDO EIOEI EJD ESBYG FEDTE FERAY FFXSO FIGPU FINBP FNLPD FRRFC FSGXE FWDCC GGCAI GGRSB GJIRD GNWQR GQ6 GQ7 GQ8 GXS H13 HF~ HG5 HG6 HMJXF HQYDN HRMNR HVGLF HZ~ I09 IHE IJ- IKXTQ ITM IWAJR IXC IZIGR IZQ I~X I~Z J-C J0Z JBSCW JCJTX JZLTJ KDC KOV KOW LAK LLZTM M4Y MA- MK~ N2Q N9A NB0 NDZJH NPVJJ NQJWS NU0 O9- O93 O9G O9I O9J OAM OVD P19 P2P P9O PF0 PT4 PT5 QOK QOS R4E R89 R9I RHV RNI RNS ROL RPX RSV RZC RZE RZK S16 S1Z S26 S27 S28 S3B SAP SCLPG SCO SDD SDH SDM SHX SISQX SJYHP SNE SNPRN SNX SOHCF SOJ SPISZ SRMVM SSLCW STPWE SZN T13 T16 TEORI TSG TSK TSV TUC TUS U2A UG4 UOJIU UTJUX UZXMN VC2 VFIZW W23 W48 WK8 YLTOR Z45 Z83 ZMTXR ZWQNP ~EX AAPKM AAYXX ABBRH ABDBE ABFSG ABJCF ABRTQ ACSTC ADHKG AEZWR AFDZB AFFHD AFHIU AFKRA AFOHR AGQPQ AHPBZ AHWEU AIXLP AMVHM ARAPS ATHPR AYFIA BENPR BGLVJ CCPQU CITATION HCIFZ K7- M7S PHGZM PHGZT PQGLB PTHSS 8FE 8FG AZQEC DWQXO GNUQQ JQ2 L6V P62 PKEHL PQEST PQQKQ PQUKI PRINS |
| ID | FETCH-LOGICAL-c363t-dfcf63c5e36a23aef6eef470c52f25d591b3290af2e87ed0e814cb40805675a63 |
| IEDL.DBID | M7S |
| ISICitedReferencesCount | 2 |
| ISICitedReferencesURI | http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=001230225000002&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| ISSN | 1019-7168 |
| IngestDate | Sat Sep 27 04:21:12 EDT 2025 Sat Nov 29 04:13:23 EST 2025 Tue Nov 18 22:07:49 EST 2025 Fri Feb 21 02:40:16 EST 2025 |
| IsDoiOpenAccess | true |
| IsOpenAccess | true |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 3 |
| Keywords | Wavelets ANOVA decomposition 41A25 Random sampling 41A63 Variable transformations 65D15 Least squares approximation 65T60 |
| Language | English |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c363t-dfcf63c5e36a23aef6eef470c52f25d591b3290af2e87ed0e814cb40805675a63 |
| Notes | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 |
| ORCID | 0000-0003-3651-4364 0000-0001-7988-1485 |
| OpenAccessLink | https://link.springer.com/10.1007/s10444-024-10147-2 |
| PQID | 3254225692 |
| PQPubID | 2043875 |
| ParticipantIDs | proquest_journals_3254225692 crossref_primary_10_1007_s10444_024_10147_2 crossref_citationtrail_10_1007_s10444_024_10147_2 springer_journals_10_1007_s10444_024_10147_2 |
| PublicationCentury | 2000 |
| PublicationDate | 20240600 2024-06-00 20240601 |
| PublicationDateYYYYMMDD | 2024-06-01 |
| PublicationDate_xml | – month: 6 year: 2024 text: 20240600 |
| PublicationDecade | 2020 |
| PublicationPlace | New York |
| PublicationPlace_xml | – name: New York |
| PublicationTitle | Advances in computational mathematics |
| PublicationTitleAbbrev | Adv Comput Math |
| PublicationYear | 2024 |
| Publisher | Springer US Springer Nature B.V |
| Publisher_xml | – name: Springer US – name: Springer Nature B.V |
| References | Schmischke, M.: Dissertation: interpretable approximation of high-dimensional data based on the ANOVA decomposition. Universitaetsverlag Chemnitz (2022) Kandasamy, K., Yu, Y.: Additive approximations in high dimensional nonparametric regression via the salsa. Int Conf Mach Learn 69–78 (2016). PMLR Gilbert, A.D., Kuo, F.Y., Sloan, I.H.: Equivalence between Sobolev spaces of first-order dominating mixed smoothness and unanchored ANOVA spaces on Rd\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb{R}^d$$\end{document}. Math. Comp. 91, 1837–1869 (2022) AdcockBHuybrechsDApproximating smooth, multivariate functions on irregular domainsForum Math. Sigma20208E26410891710.1017/fms.2020.23 DeVoreRPetrovaGWojtaszczykPApproximation of functions of few variables in high dimensionsConstr. Approx.2010331125143274705910.1007/s00365-010-9105-8 HookerGGeneralized functional ANOVA diagnostics for high-dimensional functions of dependent variablesJ. Comput. Graph. Stat.2007163709732235108710.1198/106186007X237892 XieYShiBSchaefferHWardRSHRIMP: sparser random feature models via iterative magnitude pruningMath. Sci. Mach. Learn. PMLR2022190303318 PottsDSchmischkeMInterpretable approximation of high-dimensional dataSIAM J. Math. Data Sci.20213413011323434488810.1137/21M1407707 Weidensager, L., Krumm, D., Potts, D., Odenwald, S.: Estimating vertical ground reaction forces from plantar pressure using interpretable high-dimensional approximation. Sports Eng. (accepted) (2023) SobolIMGlobal sensitivity indices for nonlinear mathematical models and their Monte Carlo estimatesMath. Comput. Simul.2001551–3271280182311910.1016/S0378-4754(00)00270-6 KühnTSickelWUllrichTApproximation numbers of Sobolev embeddings – sharp constants and tractabilityJ. Complex.20143095116316652310.1016/j.jco.2013.07.001 GriebelMKuoFYSloanIHThe smoothing effect of the ANOVA decompositionJ. Complex.2010265523551271964610.1016/j.jco.2010.04.003 HuybrechsDOn the Fourier extension of nonperiodic functionsSIAM J. Numer. Anal.201047643264355258518910.1137/090752456 DũngDTemlyakovVNUllrichTHyperbolic cross approximation2018ChamAdvanced Courses in Mathematics - CRM Barcelona. Birkhäuser10.1007/978-3-319-92240-9 RahmanSA generalized ANOVA dimensional decomposition for dependent probability measuresSIAM-ASA J. Uncertain.2014216706973283926 ChuiCKAn introduction to wavelets1992BostonAcademic Press SahaESchaefferHTranGHARFE: hard-ridge random feature expansionSampl. Theory Signal Process. Data Anal.20232127462605710.1007/s43670-023-00063-9 KuoFYSloanIHWasilkowskiGWWoźniakowskiHOn decompositions of multivariate functionsMath. Comp.201079270953966260055010.1090/S0025-5718-09-02319-9 AdcockBHuybrechsDFrames and numerical approximationSIAM Review2019613443473398923810.1137/17M1114697 HashemiASchaefferHShiRTopcuUTranGWardRGeneralization bounds for sparse random feature expansionsAppl. Comput. Harmon. Anal.202362310330449301510.1016/j.acha.2022.08.003 LiuROwenABEstimating mean dimensionality of analysis of variance decompositionsJ. Amer. Statist. Assoc.2006101474712721228124710.1198/016214505000001410 CohenAMiglioratiGOptimal weighted least-squares methodsSMAI J. Comput. Math.20173181203371675510.5802/smai-jcm.24 Triebel, H.: Theory of function spaces III. Birkhäuser Basel, 1 edition, 01 (2006) BoydJPSix strategies for defeating the Runge phenomenon in Gaussian radial basis functions on a finite intervalComput. Math. Appl.2010601231083122273947810.1016/j.camwa.2010.10.015 CaflischRMorokoffWOwenAValuation of mortgage-backed securities using Brownian bridges to reduce effective dimensionJ. Comput. Finance199711274610.21314/JCF.1997.005 Potts, D., Schmischke, M.: Interpretable transformed ANOVA approximation on the example of the prevention of forest fires. Front. Appl. Math. Stat. 8 (2022) WuCFJHamadaMSExperiments - planning, analysis, and optimization2011New YorkJohn Wiley & Sons Novak, E., Woźniakowski, H.: Tractability of Multivariate Problems Volume I: Linear Information. Eur. Math. Society, EMS Tracts in Mathematics 6 (2008) CohenADavenportMALeviatanDOn the stability and accuracy of least-squares approximationsFound. Comput. Math.201313819834310594610.1007/s10208-013-9142-3 LippertLPottsDUllrichTFast hyperbolic wavelet regression meets ANOVANumer. Math.2023154155207460965510.1007/s00211-023-01358-8 Wand, M., Jonas, M.: Kernel smoothing, vol. 60. London ; New York : Chapman & Hall (1995) BellETExponential polynomialsAnn. Math1934352258277150316110.2307/1968431 DolbeaultMCohenAOptimal pointwise sampling for l2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$l^2$$\end{document} approximationJ. Complex.20226810.1016/j.jco.2021.101602 Holtz, M.: Sparse grid quadrature in high dimensions with applications in finance and insurance. Lecture Notes in Computational Science and Engineering, vol. 77. Springer-Verlag, Berlin (2011) Nasdala, R.: Efficient multivariate approximation with transformed rank-1 lattices. Dissertation, Fakultät für Mathematik, Technische Universität Chemnitz (2021) KämmererLUllrichTVolkmerTWorst case recovery guarantees for least squares approximation using random samplesConstr. Approx.202154295352432177610.1007/s00365-021-09555-0 JiaR-QSpline wavelets on the interval with homogeneous boundary conditionsAdv. Comput. Math.200930177200247144710.1007/s10444-008-9064-9 RahmanSApproximation errors in truncated dimensional decompositionsMath. Comput.20148329027992819324681010.1090/S0025-5718-2014-02883-4 AdcockBBrugiapagliaSWebsterCGSparse polynomial approximation of high-dimensional functions2022Philadelphia, PennsylvaniaComputational science & engineering. SIAM10.1137/1.9781611976885 DahmenWKunothAUrbanKBiorthogonal spline wavelets on the interval-stability and moment conditionsAppl. Comput. Harmon. Anal.199962132196167677110.1006/acha.1998.0247 NuyensDSuzukiYScaled lattice rules for integration on Rd\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb{R} ^d$$\end{document} achieving higher-order convergence with error analysis in terms of orthogonal projections onto periodic spacesMath. Comp.202392307347449696710.1090/mcom/3754 PottsDSchmischkeMApproximation of high-dimensional periodic functions with Fourier-based methodsSIAM J. Numer. Anal.202159523932429431384710.1137/20M1354921 Gramacki, A.: Nonparametric kernel density estimation and its computational aspects, vol. 37. Springer International (2018) SheatherSJJonesMCA reliable data-based bandwidth selection method for kernel density estimationJ. R. Stat. Soc. Ser. B Methodol.199153683690112572510.1111/j.2517-6161.1991.tb01857.x D Dũng (10147_CR10) 2018 S Rahman (10147_CR34) 2014; 83 10147_CR41 10147_CR42 10147_CR40 G Hooker (10147_CR19) 2007; 16 A Hashemi (10147_CR17) 2023; 62 10147_CR28 FY Kuo (10147_CR25) 2010; 79 10147_CR23 D Huybrechs (10147_CR20) 2010; 47 A Cohen (10147_CR8) 2013; 13 T Kühn (10147_CR24) 2014; 30 IM Sobol (10147_CR39) 2001; 55 L Kämmerer (10147_CR22) 2021; 54 10147_CR18 R Liu (10147_CR27) 2006; 101 M Dolbeault (10147_CR13) 2022; 68 E Saha (10147_CR36) 2023; 21 CK Chui (10147_CR7) 1992 D Nuyens (10147_CR30) 2023; 92 D Potts (10147_CR32) 2021; 3 B Adcock (10147_CR3) 2020; 8 SJ Sheather (10147_CR38) 1991; 53 10147_CR14 10147_CR15 10147_CR37 ET Bell (10147_CR4) 1934; 35 Y Xie (10147_CR44) 2022; 190 B Adcock (10147_CR1) 2022 10147_CR33 S Rahman (10147_CR35) 2014; 2 CFJ Wu (10147_CR43) 2011 A Cohen (10147_CR9) 2017; 3 10147_CR29 R DeVore (10147_CR12) 2010; 33 R-Q Jia (10147_CR21) 2009; 30 W Dahmen (10147_CR11) 1999; 6 L Lippert (10147_CR26) 2023; 154 JP Boyd (10147_CR5) 2010; 60 D Potts (10147_CR31) 2021; 59 B Adcock (10147_CR2) 2019; 61 R Caflisch (10147_CR6) 1997; 1 M Griebel (10147_CR16) 2010; 26 |
| References_xml | – reference: KämmererLUllrichTVolkmerTWorst case recovery guarantees for least squares approximation using random samplesConstr. Approx.202154295352432177610.1007/s00365-021-09555-0 – reference: HuybrechsDOn the Fourier extension of nonperiodic functionsSIAM J. Numer. Anal.201047643264355258518910.1137/090752456 – reference: PottsDSchmischkeMInterpretable approximation of high-dimensional dataSIAM J. Math. Data Sci.20213413011323434488810.1137/21M1407707 – reference: PottsDSchmischkeMApproximation of high-dimensional periodic functions with Fourier-based methodsSIAM J. Numer. Anal.202159523932429431384710.1137/20M1354921 – reference: KuoFYSloanIHWasilkowskiGWWoźniakowskiHOn decompositions of multivariate functionsMath. Comp.201079270953966260055010.1090/S0025-5718-09-02319-9 – reference: RahmanSApproximation errors in truncated dimensional decompositionsMath. Comput.20148329027992819324681010.1090/S0025-5718-2014-02883-4 – reference: SobolIMGlobal sensitivity indices for nonlinear mathematical models and their Monte Carlo estimatesMath. Comput. Simul.2001551–3271280182311910.1016/S0378-4754(00)00270-6 – reference: XieYShiBSchaefferHWardRSHRIMP: sparser random feature models via iterative magnitude pruningMath. Sci. Mach. Learn. PMLR2022190303318 – reference: Kandasamy, K., Yu, Y.: Additive approximations in high dimensional nonparametric regression via the salsa. Int Conf Mach Learn 69–78 (2016). PMLR – reference: KühnTSickelWUllrichTApproximation numbers of Sobolev embeddings – sharp constants and tractabilityJ. Complex.20143095116316652310.1016/j.jco.2013.07.001 – reference: Triebel, H.: Theory of function spaces III. Birkhäuser Basel, 1 edition, 01 (2006) – reference: Wand, M., Jonas, M.: Kernel smoothing, vol. 60. London ; New York : Chapman & Hall (1995) – reference: SheatherSJJonesMCA reliable data-based bandwidth selection method for kernel density estimationJ. R. Stat. Soc. Ser. B Methodol.199153683690112572510.1111/j.2517-6161.1991.tb01857.x – reference: DolbeaultMCohenAOptimal pointwise sampling for l2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$l^2$$\end{document} approximationJ. Complex.20226810.1016/j.jco.2021.101602 – reference: WuCFJHamadaMSExperiments - planning, analysis, and optimization2011New YorkJohn Wiley & Sons – reference: SahaESchaefferHTranGHARFE: hard-ridge random feature expansionSampl. Theory Signal Process. Data Anal.20232127462605710.1007/s43670-023-00063-9 – reference: LiuROwenABEstimating mean dimensionality of analysis of variance decompositionsJ. Amer. Statist. Assoc.2006101474712721228124710.1198/016214505000001410 – reference: ChuiCKAn introduction to wavelets1992BostonAcademic Press – reference: DeVoreRPetrovaGWojtaszczykPApproximation of functions of few variables in high dimensionsConstr. Approx.2010331125143274705910.1007/s00365-010-9105-8 – reference: Gilbert, A.D., Kuo, F.Y., Sloan, I.H.: Equivalence between Sobolev spaces of first-order dominating mixed smoothness and unanchored ANOVA spaces on Rd\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb{R}^d$$\end{document}. Math. Comp. 91, 1837–1869 (2022) – reference: DahmenWKunothAUrbanKBiorthogonal spline wavelets on the interval-stability and moment conditionsAppl. Comput. Harmon. Anal.199962132196167677110.1006/acha.1998.0247 – reference: Gramacki, A.: Nonparametric kernel density estimation and its computational aspects, vol. 37. Springer International (2018) – reference: HashemiASchaefferHShiRTopcuUTranGWardRGeneralization bounds for sparse random feature expansionsAppl. Comput. Harmon. Anal.202362310330449301510.1016/j.acha.2022.08.003 – reference: LippertLPottsDUllrichTFast hyperbolic wavelet regression meets ANOVANumer. Math.2023154155207460965510.1007/s00211-023-01358-8 – reference: HookerGGeneralized functional ANOVA diagnostics for high-dimensional functions of dependent variablesJ. Comput. Graph. Stat.2007163709732235108710.1198/106186007X237892 – reference: GriebelMKuoFYSloanIHThe smoothing effect of the ANOVA decompositionJ. Complex.2010265523551271964610.1016/j.jco.2010.04.003 – reference: Potts, D., Schmischke, M.: Interpretable transformed ANOVA approximation on the example of the prevention of forest fires. Front. Appl. Math. Stat. 8 (2022) – reference: BellETExponential polynomialsAnn. Math1934352258277150316110.2307/1968431 – reference: CohenADavenportMALeviatanDOn the stability and accuracy of least-squares approximationsFound. Comput. Math.201313819834310594610.1007/s10208-013-9142-3 – reference: CohenAMiglioratiGOptimal weighted least-squares methodsSMAI J. Comput. Math.20173181203371675510.5802/smai-jcm.24 – reference: Holtz, M.: Sparse grid quadrature in high dimensions with applications in finance and insurance. Lecture Notes in Computational Science and Engineering, vol. 77. Springer-Verlag, Berlin (2011) – reference: RahmanSA generalized ANOVA dimensional decomposition for dependent probability measuresSIAM-ASA J. Uncertain.2014216706973283926 – reference: AdcockBHuybrechsDApproximating smooth, multivariate functions on irregular domainsForum Math. Sigma20208E26410891710.1017/fms.2020.23 – reference: Schmischke, M.: Dissertation: interpretable approximation of high-dimensional data based on the ANOVA decomposition. Universitaetsverlag Chemnitz (2022) – reference: Novak, E., Woźniakowski, H.: Tractability of Multivariate Problems Volume I: Linear Information. Eur. Math. Society, EMS Tracts in Mathematics 6 (2008) – reference: AdcockBBrugiapagliaSWebsterCGSparse polynomial approximation of high-dimensional functions2022Philadelphia, PennsylvaniaComputational science & engineering. SIAM10.1137/1.9781611976885 – reference: NuyensDSuzukiYScaled lattice rules for integration on Rd\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb{R} ^d$$\end{document} achieving higher-order convergence with error analysis in terms of orthogonal projections onto periodic spacesMath. Comp.202392307347449696710.1090/mcom/3754 – reference: Weidensager, L., Krumm, D., Potts, D., Odenwald, S.: Estimating vertical ground reaction forces from plantar pressure using interpretable high-dimensional approximation. Sports Eng. (accepted) (2023) – reference: AdcockBHuybrechsDFrames and numerical approximationSIAM Review2019613443473398923810.1137/17M1114697 – reference: JiaR-QSpline wavelets on the interval with homogeneous boundary conditionsAdv. Comput. Math.200930177200247144710.1007/s10444-008-9064-9 – reference: BoydJPSix strategies for defeating the Runge phenomenon in Gaussian radial basis functions on a finite intervalComput. Math. Appl.2010601231083122273947810.1016/j.camwa.2010.10.015 – reference: CaflischRMorokoffWOwenAValuation of mortgage-backed securities using Brownian bridges to reduce effective dimensionJ. Comput. Finance199711274610.21314/JCF.1997.005 – reference: DũngDTemlyakovVNUllrichTHyperbolic cross approximation2018ChamAdvanced Courses in Mathematics - CRM Barcelona. Birkhäuser10.1007/978-3-319-92240-9 – reference: Nasdala, R.: Efficient multivariate approximation with transformed rank-1 lattices. Dissertation, Fakultät für Mathematik, Technische Universität Chemnitz (2021) – volume: 61 start-page: 443 issue: 3 year: 2019 ident: 10147_CR2 publication-title: SIAM Review doi: 10.1137/17M1114697 – volume: 35 start-page: 258 issue: 2 year: 1934 ident: 10147_CR4 publication-title: Ann. Math doi: 10.2307/1968431 – volume: 6 start-page: 132 issue: 2 year: 1999 ident: 10147_CR11 publication-title: Appl. Comput. Harmon. Anal. doi: 10.1006/acha.1998.0247 – volume: 30 start-page: 95 year: 2014 ident: 10147_CR24 publication-title: J. Complex. doi: 10.1016/j.jco.2013.07.001 – volume: 79 start-page: 953 issue: 270 year: 2010 ident: 10147_CR25 publication-title: Math. Comp. doi: 10.1090/S0025-5718-09-02319-9 – volume: 59 start-page: 2393 issue: 5 year: 2021 ident: 10147_CR31 publication-title: SIAM J. Numer. Anal. doi: 10.1137/20M1354921 – volume: 8 start-page: E26 year: 2020 ident: 10147_CR3 publication-title: Forum Math. Sigma doi: 10.1017/fms.2020.23 – volume: 83 start-page: 2799 issue: 290 year: 2014 ident: 10147_CR34 publication-title: Math. Comput. doi: 10.1090/S0025-5718-2014-02883-4 – volume: 62 start-page: 310 year: 2023 ident: 10147_CR17 publication-title: Appl. Comput. Harmon. Anal. doi: 10.1016/j.acha.2022.08.003 – volume: 16 start-page: 709 issue: 3 year: 2007 ident: 10147_CR19 publication-title: J. Comput. Graph. Stat. doi: 10.1198/106186007X237892 – volume: 30 start-page: 177 year: 2009 ident: 10147_CR21 publication-title: Adv. Comput. Math. doi: 10.1007/s10444-008-9064-9 – volume: 68 year: 2022 ident: 10147_CR13 publication-title: J. Complex. doi: 10.1016/j.jco.2021.101602 – ident: 10147_CR15 doi: 10.1007/978-3-319-71688-6 – ident: 10147_CR23 – ident: 10147_CR40 – ident: 10147_CR41 doi: 10.1007/978-1-4899-4493-1 – volume: 21 start-page: 27 year: 2023 ident: 10147_CR36 publication-title: Sampl. Theory Signal Process. Data Anal. doi: 10.1007/s43670-023-00063-9 – volume: 2 start-page: 670 issue: 1 year: 2014 ident: 10147_CR35 publication-title: SIAM-ASA J. Uncertain. – volume-title: Experiments - planning, analysis, and optimization year: 2011 ident: 10147_CR43 – volume: 3 start-page: 181 year: 2017 ident: 10147_CR9 publication-title: SMAI J. Comput. Math. doi: 10.5802/smai-jcm.24 – volume: 47 start-page: 4326 issue: 6 year: 2010 ident: 10147_CR20 publication-title: SIAM J. Numer. Anal. doi: 10.1137/090752456 – volume: 1 start-page: 27 issue: 1 year: 1997 ident: 10147_CR6 publication-title: J. Comput. Finance doi: 10.21314/JCF.1997.005 – volume: 13 start-page: 819 year: 2013 ident: 10147_CR8 publication-title: Found. Comput. Math. doi: 10.1007/s10208-013-9142-3 – ident: 10147_CR29 doi: 10.4171/026 – volume: 154 start-page: 155 year: 2023 ident: 10147_CR26 publication-title: Numer. Math. doi: 10.1007/s00211-023-01358-8 – volume: 55 start-page: 271 issue: 1–3 year: 2001 ident: 10147_CR39 publication-title: Math. Comput. Simul. doi: 10.1016/S0378-4754(00)00270-6 – volume: 26 start-page: 523 issue: 5 year: 2010 ident: 10147_CR16 publication-title: J. Complex. doi: 10.1016/j.jco.2010.04.003 – ident: 10147_CR18 doi: 10.1007/978-3-642-16004-2 – ident: 10147_CR42 doi: 10.1007/s12283-023-00444-2 – ident: 10147_CR14 doi: 10.1090/mcom/3718 – volume: 54 start-page: 295 year: 2021 ident: 10147_CR22 publication-title: Constr. Approx. doi: 10.1007/s00365-021-09555-0 – volume-title: Hyperbolic cross approximation year: 2018 ident: 10147_CR10 doi: 10.1007/978-3-319-92240-9 – ident: 10147_CR33 doi: 10.3389/fams.2022.795250 – volume: 3 start-page: 1301 issue: 4 year: 2021 ident: 10147_CR32 publication-title: SIAM J. Math. Data Sci. doi: 10.1137/21M1407707 – volume: 60 start-page: 3108 issue: 12 year: 2010 ident: 10147_CR5 publication-title: Comput. Math. Appl. doi: 10.1016/j.camwa.2010.10.015 – volume-title: Sparse polynomial approximation of high-dimensional functions year: 2022 ident: 10147_CR1 doi: 10.1137/1.9781611976885 – ident: 10147_CR28 – volume: 33 start-page: 125 issue: 1 year: 2010 ident: 10147_CR12 publication-title: Constr. Approx. doi: 10.1007/s00365-010-9105-8 – volume: 101 start-page: 712 issue: 474 year: 2006 ident: 10147_CR27 publication-title: J. Amer. Statist. Assoc. doi: 10.1198/016214505000001410 – volume: 190 start-page: 303 year: 2022 ident: 10147_CR44 publication-title: Math. Sci. Mach. Learn. PMLR – volume-title: An introduction to wavelets year: 1992 ident: 10147_CR7 – volume: 53 start-page: 683 year: 1991 ident: 10147_CR38 publication-title: J. R. Stat. Soc. Ser. B Methodol. doi: 10.1111/j.2517-6161.1991.tb01857.x – volume: 92 start-page: 307 year: 2023 ident: 10147_CR30 publication-title: Math. Comp. doi: 10.1090/mcom/3754 – ident: 10147_CR37 |
| SSID | ssj0009675 |
| Score | 2.3799958 |
| Snippet | We use hyperbolic wavelet regression for the fast reconstruction of high-dimensional functions having only low-dimensional variable interactions. Compactly... |
| SourceID | proquest crossref springer |
| SourceType | Aggregation Database Enrichment Source Index Database Publisher |
| StartPage | 53 |
| SubjectTerms | Approximation Computational Mathematics and Numerical Analysis Computational Science and Engineering Density functions Least squares method Mathematical and Computational Biology Mathematical Modeling and Industrial Mathematics Mathematics Mathematics and Statistics Periodic functions Polynomials Statistical analysis Toruses Transformations (mathematics) Variance analysis Visualization |
| SummonAdditionalLinks | – databaseName: SpringerLINK Contemporary 1997-Present dbid: RSV link: http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV3NS8MwFA-iHvTgdCpOp-TgTQNrkqbtcYjDg07xY-xWkjSBgVRZ68ef70vablNU0GPJR8t7L3m_l_T9HkLHVguaKMoIi5WEAMUwojIdEUDLVGllReyJtEeX0XAYj8fJTZ0UVjR_uzdXkn6nXkh245wT8CnE1ZeNCGy8K-DuYlew4fZuNKfaFZ5eFzolBKKBuE6V-X6Oz-5ojjG_XIt6bzNo_e87N9FGjS5xvzKHLbRk8jZq1UgT1-u4aKP1qxlba7GN1AgCZpdChcsFGAvmiCc5hpdC8OyfsTu0xW_S1aooCyzzDPeH16M-hhHY8R6TzNUKqHg-sGcrf59UU-2gh8H5_dkFqWsvEM0EK0lmtRVMh4YJSZk0VhhjedTTIbU0zMIkUIwmPWmpiSOT9UwccK044M8QxC8F20XL-VNu9hA2AZcAFJjRYcKTwCpugizWvUwHlqtIdlDQqCDVNTG5q4_xmM4plZ1IUxBp6kWa0g46mY15rmg5fu3dbTSb1ku0SBmExrCZiQSaTxtNzpt_nm3_b90P0Bp1xuBPbrpouZy-mEO0ql_LSTE98qb7AbiU6GE priority: 102 providerName: Springer Nature |
| Title | Variable transformations in combination with wavelets and ANOVA for high-dimensional approximation |
| URI | https://link.springer.com/article/10.1007/s10444-024-10147-2 https://www.proquest.com/docview/3254225692 |
| Volume | 50 |
| WOSCitedRecordID | wos001230225000002&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| journalDatabaseRights | – providerCode: PRVPQU databaseName: Advanced Technologies & Aerospace Database customDbUrl: eissn: 1572-9044 dateEnd: 20241212 omitProxy: false ssIdentifier: ssj0009675 issn: 1019-7168 databaseCode: P5Z dateStart: 20230201 isFulltext: true titleUrlDefault: https://search.proquest.com/hightechjournals providerName: ProQuest – providerCode: PRVPQU databaseName: Computer Science Database customDbUrl: eissn: 1572-9044 dateEnd: 20241212 omitProxy: false ssIdentifier: ssj0009675 issn: 1019-7168 databaseCode: K7- dateStart: 20230201 isFulltext: true titleUrlDefault: http://search.proquest.com/compscijour providerName: ProQuest – providerCode: PRVPQU databaseName: Engineering Database customDbUrl: eissn: 1572-9044 dateEnd: 20241212 omitProxy: false ssIdentifier: ssj0009675 issn: 1019-7168 databaseCode: M7S dateStart: 20230201 isFulltext: true titleUrlDefault: http://search.proquest.com providerName: ProQuest – providerCode: PRVPQU databaseName: ProQuest Central customDbUrl: eissn: 1572-9044 dateEnd: 20241212 omitProxy: false ssIdentifier: ssj0009675 issn: 1019-7168 databaseCode: BENPR dateStart: 20230201 isFulltext: true titleUrlDefault: https://www.proquest.com/central providerName: ProQuest – providerCode: PRVAVX databaseName: SpringerLINK Contemporary 1997-Present customDbUrl: eissn: 1572-9044 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0009675 issn: 1019-7168 databaseCode: RSV dateStart: 19970101 isFulltext: true titleUrlDefault: https://link.springer.com/search?facet-content-type=%22Journal%22 providerName: Springer Nature |
| link | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV1NT9wwEB2VjwOX0lJQl9KVD9yoxcZ2nOSEtghUqdV2BXSFuET-lFZCWUpS2p_P2OttaKVy6SVSlNiJPGP7zdh-D-DQG8kqzTjlpVYYoDhOtTUFRbTMtNFelpFIe_almEzK6-tqmhJubdpWuRoT40BtFybkyI85RjLoe7JiJ3ffaVCNCqurSUJjDTYCS0IWt-5d9qS7MhLtotdVFOOCMh2aSUfnhBAUZyga1GoLyv6cmHq0-dcCaZx3zrf_949fwcuEOMl46SKv4YVrdmA7oU-S-nb7BvQMw-ZwkIp0T8AsOiWZNwS_iCF0vCchdUt-qqBY0bVENZaMJ19nY4IlSGA_pjYoBizZPkjkLP81X1a1C9_Oz65OP9GkwEANl7yj1hsvuckdl4px5bx0zotiZHLmWW7zKtOcVSPlmSsLZ0euzITRAlFojk2vJN-D9WbRuLdAXCYUwgXuTF6JKvNauMyWZmRN5oUu1ACyVfPXJtGTB5WM27onVg4mq9FkdTRZzQZw9LvM3ZKc49m3D1Z2qlNHbeveSAP4sLJ0__jfte0_X9s72GLBuWK-5gDWu_sf7j1smodu3t4PYePj2WR6MYS1zwUdRqfF6zS_wevF5ewRN8Dyew |
| linkProvider | ProQuest |
| linkToHtml | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMw1V1NT9wwEB0BrUQvpaWtugWKD3CiVje24ySHqlqVItBuFw50xS31p7QSCpQEaP8Uv7HjfBBaqdw4cE48kuM34zfj-A3AljeSZZpxylOtMEFxnGprEopsmWmjvUxrIe3ZJJlO05OT7GgBbrq7MOG3yi4m1oHanplQI__IMZNB7MmMfT7_SUPXqHC62rXQaGAxdr-vMWUrPx3s4vpuM7b39fjLPm27ClDDJa-o9cZLbmLHpWJcOS-d8yIZmph5Fts4izRn2VB55tLE2aFLI2G0QGYVI7lWkqPdRXgieJoEvxontBf5lbWwL6I8o5iHpO0lnfaqnhCC4o5IQ3fchLK_N8Ke3f5zIFvvc3srj-0LvYDnLaMmo8YFXsKCK1ZhpWXXpI1d5SvQM4XOpk8dqe6QdXQ6Mi8IzlDPm8IoCaVpcq1CR46qJKqwZDQ9nI0IjiBB3Zna0BGhUTMhtSb7r3lj6jV8f5CZvoGl4qxwb4G4SCikQ9yZOBNZ5LVwkU3N0JrIC52oAUTdcuemlV8PXUBO8144OkAkR4jkNURyNoCd2zHnjfjIvW-vd7jI20BU5j0oBvChQ1b_-P_W3t1vbROW94-_TfLJwXS8Bs9YAHZdm1qHperi0m3AU3NVzcuL97WLEPjx0Ij7A_-TS38 |
| linkToPdf | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV1LS8QwEA6iInrwLb7NwZsGt0matsdFXRR1FdTFW8kTFqSKrY-f7yTtuquoIB5DkiFkJsk3SeYbhHadFjRTlBGWKgkOimVEGZ0QQMtUaeVEGoi0e-dJt5ve3WVXI1H84bf74EmyjmnwLE1FdfBo3MFI4BvnnMD5Qnyu2YTAJjzB_Ud6769f94a0uyJQ7UKjjIBnkDZhM9_L-Hw0DfHmlyfScPJ05v4_5nk026BO3K7NZAGN2WIRzTUIFDfru1xEMxcfLK7lElI9cKR9aBWuRuAtmCnuFxgGAE51KGN_mYtfpc9hUZVYFga3u5e9NoYe2PMhE-NzCNT8HziwmL_1a1HL6LZzfHN4QpqcDEQzwSpinHaC6dgyISmT1glrHU9aOqaOxibOIsVo1pKO2jSxpmXTiGvFAZfGoAop2AoaLx4Ku4qwjbgEAMGsjjOeRU5xG5lUt4yOHFeJXEPRQB25bgjLfd6M-3xIteynNIcpzcOU5nQN7X30eazpOn5tvTnQct4s3TJn4DLDJicyqN4faHVY_bO09b8130FTV0ed_Py0e7aBpqm3i3C5s4nGq6dnu4Um9UvVL5-2g0W_AzBX9Ck |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Variable+transformations+in+combination+with+wavelets+and+ANOVA+for+high-dimensional+approximation&rft.jtitle=Advances+in+computational+mathematics&rft.au=Potts%2C+Daniel&rft.au=Weidensager%2C+Laura&rft.date=2024-06-01&rft.pub=Springer+Nature+B.V&rft.issn=1019-7168&rft.eissn=1572-9044&rft.volume=50&rft.issue=3&rft.spage=53&rft_id=info:doi/10.1007%2Fs10444-024-10147-2 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=1019-7168&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=1019-7168&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=1019-7168&client=summon |