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Distributed multi-agent Gaussian regression via finite-dimensional approximations
Information Engineering, University of Padova.
Department of Information Engineering, University of Padova.
Luleå University of Technology, Department of Computer Science, Electrical and Space Engineering, Signals and Systems.ORCID iD: 0000-0002-4310-7938
2018 (English)In: IEEE Transaction on Pattern Analysis and Machine Intelligence, ISSN 0162-8828, E-ISSN 1939-3539Article in journal (Refereed) Epub ahead of print
Abstract [en]

We consider the problem of distributedly estimating Gaussian processes in multi-agent frameworks. Each agent collects few measurements and aims to collaboratively reconstruct a common estimate based on all data. Agents are assumed with limited computational and communication capabilities and to gather <formula><tex>$M$</tex></formula>noisy measurements in total on input locations independently drawn from a known common probability density. The optimal solution would require agents to exchange all the <formula><tex>$M$</tex></formula>input locations and measurements and then invert an <formula><tex>$M\times M$</tex></formula> matrix, a non-scalable task. Differently, we propose two suboptimal approaches using the first <formula><tex>$E$</tex></formula> orthonormal eigenfunctions obtained from the KL expansion of the chosen kernel, where typically <formula><tex>$E\ll M$</tex></formula>. The benefits are that the computation and communication complexities scale with <formula><tex>$E$</tex></formula> and not with <formula><tex>$M$</tex></formula>, and computing the required statistics can be performed via standard average consensus algorithms. We obtain probabilistic non-asymptotic bounds that determine a priori the desired level of estimation accuracy, and new distributed strategies relying on SURE paradigms for tuning the regularization parameters and applicable to generic basis functions (thus not necessarily kernel eigenfunctions) and that can again be implemented via average consensus. The proposed estimators and bounds are finally tested on both synthetic and real field data. OAPA

Place, publisher, year, edition, pages
2018.
National Category
Control Engineering
Research subject
Control Engineering
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URN: urn:nbn:se:ltu:diva-69896DOI: 10.1109/TPAMI.2018.2836422OAI: oai:DiVA.org:ltu-69896DiVA, id: diva2:1224170
Available from: 2018-06-26 Created: 2018-06-26 Last updated: 2018-06-26

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Varagnolo, Damiano

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