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Statistical bounds for Gaussian regression algorithms based on Karhunen-Loève expansions
Department of Information Engineering, University of Padova, Padova, Italy.
Department of Information Engineering, University of Padova, Padova, Italy.
Luleå University of Technology, Department of Computer Science, Electrical and Space Engineering, Signals and Systems.ORCID iD: 0000-0002-4310-7938
2018 (English)In: 2017 IEEE 56th Conference on Decision and Control, CDC, Piscataway, NJ: Institute of Electrical and Electronics Engineers (IEEE), 2018, p. 363-368Conference paper, Published paper (Refereed)
Abstract [en]

We consider the problem of estimating functions in a Gaussian regression distributed and nonparametric framework where the unknown map is modeled as a Gaussian random field whose kernel encodes expected properties like smoothness. We assume that some agents with limited computational and communication capabilities collect M noisy function measurements on input locations independently drawn from a known probability density. Collaboration is then needed to obtain a common and shared estimate. When the number of measurements M is large, computing the minimum variance estimate in a distributed fashion is difficult since it requires first to exchange all the measurements and then to invert an M χ M matrix. A common approach is then to circumvent this problem by searching a suboptimal solution within a subspace spanned by a finite number of kernel eigenfunctions. In this paper we analyze this classical distributed estimator, and derive a rigorous probabilistic bound on its statistical performance that returns crucial information on the number of measurements and eigenfunctions needed to obtain the desired level of estimation accuracy.

Place, publisher, year, edition, pages
Piscataway, NJ: Institute of Electrical and Electronics Engineers (IEEE), 2018. p. 363-368
Series
IEEE Conference on Decision and Control, E-ISSN 0743-1546
National Category
Control Engineering
Research subject
Control Engineering
Identifiers
URN: urn:nbn:se:ltu:diva-67652DOI: 10.1109/CDC.2017.8263691ISI: 000424696900058Scopus ID: 2-s2.0-85046159489ISBN: 978-1-5090-2873-3 (electronic)ISBN: 978-1-5090-2874-0 (print)OAI: oai:DiVA.org:ltu-67652DiVA, id: diva2:1182707
Conference
56th IEEE Conference on Decision and Control, CDC 2017, Melbourne, VIC, Australia , 12-15 December 2017
Available from: 2018-02-14 Created: 2018-02-14 Last updated: 2018-05-09Bibliographically approved

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Pillonetto, GianluigiSchenato, Luca

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  • apa
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