{"data":{"id":"10.6084/m9.figshare.1582730","type":"dois","attributes":{"doi":"10.6084/m9.figshare.1582730","prefix":"10.6084","suffix":"m9.figshare.1582730","identifiers":[],"alternateIdentifiers":[],"creators":[{"name":"Izbicki, Rafael","nameType":"Personal","givenName":"Rafael","familyName":"Izbicki","affiliation":[],"nameIdentifiers":[]},{"name":"Lee, Ann B.","nameType":"Personal","givenName":"Ann B.","familyName":"Lee","affiliation":[],"nameIdentifiers":[]}],"titles":[{"title":"Nonparametric Conditional Density Estimation in a High-Dimensional Regression Setting"}],"publisher":"Taylor \u0026 Francis","container":{},"publicationYear":2015,"subjects":[{"subject":"Molecular Biology"},{"subject":"Biotechnology"},{"subject":"39999 Chemical Sciences not elsewhere classified","subjectScheme":"FOR"},{"subject":"FOS: Chemical sciences","schemeUri":"http://www.oecd.org/science/inno/38235147.pdf","subjectScheme":"Fields of Science and Technology (FOS)"},{"subject":"FOS: Chemical sciences","subjectScheme":"Fields of Science and Technology (FOS)"},{"subject":"Ecology"},{"subject":"FOS: Biological sciences","schemeUri":"http://www.oecd.org/science/inno/38235147.pdf","subjectScheme":"Fields of Science and Technology (FOS)"},{"subject":"FOS: Biological sciences","subjectScheme":"Fields of Science and Technology (FOS)"},{"subject":"19999 Mathematical Sciences not elsewhere classified","subjectScheme":"FOR"},{"subject":"FOS: Mathematics","schemeUri":"http://www.oecd.org/science/inno/38235147.pdf","subjectScheme":"Fields of Science and Technology (FOS)"},{"subject":"FOS: Mathematics","subjectScheme":"Fields of Science and Technology (FOS)"},{"subject":"Marine Biology"},{"subject":"Plant Biology"}],"contributors":[],"dates":[{"date":"2015-10-22","dateType":"Created"},{"date":"2016-11-10","dateType":"Updated"},{"date":"2015","dateType":"Issued"}],"language":null,"types":{"ris":"DATA","bibtex":"misc","citeproc":"dataset","schemaOrg":"Dataset","resourceType":"Dataset","resourceTypeGeneral":"Dataset"},"relatedIdentifiers":[{"relationType":"IsSupplementTo","relatedIdentifier":"10.1080/10618600.2015.1094393","relatedIdentifierType":"DOI"}],"relatedItems":[],"sizes":["98213419 Bytes"],"formats":[],"version":null,"rightsList":[{"rights":"Creative Commons Attribution 4.0 International","rightsUri":"https://creativecommons.org/licenses/by/4.0/legalcode","schemeUri":"https://spdx.org/licenses/","rightsIdentifier":"cc-by-4.0","rightsIdentifierScheme":"SPDX"}],"descriptions":[{"description":"In some applications (e.g., in cosmology and economics), the regression E[Z|x] is not adequate to represent the association between a predictor \u003cb\u003ex\u003c/b\u003e and a response \u003ci\u003eZ\u003c/i\u003e because of multi-modality and asymmetry of \u003ci\u003ef\u003c/i\u003e(\u003ci\u003ez\u003c/i\u003e|\u003cb\u003ex\u003c/b\u003e); using the full density instead of a single-point estimate can then lead to less bias in subsequent analysis. As of now, there are no effective ways of estimating \u003ci\u003ef\u003c/i\u003e(\u003ci\u003ez\u003c/i\u003e|\u003cb\u003ex\u003c/b\u003e) when \u003cb\u003ex\u003c/b\u003e represents high-dimensional, complex data. In this article, we propose a new nonparametric estimator of \u003ci\u003ef\u003c/i\u003e(\u003ci\u003ez\u003c/i\u003e|\u003cb\u003ex\u003c/b\u003e) that adapts to sparse (low-dimensional) structure in \u003cb\u003ex\u003c/b\u003e. By directly expanding \u003ci\u003ef\u003c/i\u003e(\u003ci\u003ez\u003c/i\u003e|\u003cb\u003ex\u003c/b\u003e) in the eigenfunctions of a kernel-based operator, we avoid tensor products in high dimensions as well as ratios of estimated densities. Our basis functions are orthogonal with respect to the underlying data distribution, allowing fast implementation and tuning of parameters. We derive rates of convergence and show that the method adapts to the intrinsic dimension of the data. We also demonstrate the effectiveness of the series method on images, spectra, and an application to photometric redshift estimation of galaxies. Supplementary materials for this article are available online.","descriptionType":"Abstract"}],"geoLocations":[],"fundingReferences":[],"xml":"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","url":"https://tandf.figshare.com/articles/dataset/Nonparametric_Conditional_Density_Estim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