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http://dx.doi.org/10.18419/opus-13663
Autor(en): | Györfi, László Linder, Tamás Walk, Harro |
Titel: | Lossless transformations and excess risk bounds in statistical inference |
Erscheinungsdatum: | 2023 |
Dokumentart: | Zeitschriftenartikel |
Seiten: | 25 |
Erschienen in: | Entropy 25 (2023), No. 1394 |
URI: | http://nbn-resolving.de/urn:nbn:de:bsz:93-opus-ds-136826 http://elib.uni-stuttgart.de/handle/11682/13682 http://dx.doi.org/10.18419/opus-13663 |
ISSN: | 1099-4300 |
Zusammenfassung: | We study the excess minimum risk in statistical inference, defined as the difference between the minimum expected loss when estimating a random variable from an observed feature vector and the minimum expected loss when estimating the same random variable from a transformation (statistic) of the feature vector. After characterizing lossless transformations, i.e., transformations for which the excess risk is zero for all loss functions, we construct a partitioning test statistic for the hypothesis that a given transformation is lossless, and we show that for i.i.d. data the test is strongly consistent. More generally, we develop information-theoretic upper bounds on the excess risk that uniformly hold over fairly general classes of loss functions. Based on these bounds, we introduce the notion of a δ -lossless transformation and give sufficient conditions for a given transformation to be universally δ -lossless. Applications to classification, nonparametric regression, portfolio strategies, information bottlenecks, and deep learning are also surveyed. |
Enthalten in den Sammlungen: | 08 Fakultät Mathematik und Physik |
Dateien zu dieser Ressource:
Datei | Beschreibung | Größe | Format | |
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entropy-25-01394-v2.pdf | 389,84 kB | Adobe PDF | Öffnen/Anzeigen |
Diese Ressource wurde unter folgender Copyright-Bestimmung veröffentlicht: Lizenz von Creative Commons