Local Linear Regression for Function Learning: An Analysis Based on Sample Discrepancy (Articolo in rivista)

Type
Label
  • Local Linear Regression for Function Learning: An Analysis Based on Sample Discrepancy (Articolo in rivista) (literal)
Anno
  • 2014-01-01T00:00:00+01:00 (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#doi
  • 10.1109/TNNLS.2014.2305193 (literal)
Alternative label
  • Cristiano, Cervellera; Danilo, Macciò (2014)
    Local Linear Regression for Function Learning: An Analysis Based on Sample Discrepancy
    in IEEE Transactions on Neural Networks and Learning Systems
    (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#autori
  • Cristiano, Cervellera; Danilo, Macciò (literal)
Pagina inizio
  • 2086 (literal)
Pagina fine
  • 2098 (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#altreInformazioni
  • Quartile della rivista: Q1, nel settore \"Artificial Intelligence\". (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#numeroVolume
  • 25 (literal)
Rivista
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#pagineTotali
  • 13 (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#numeroFascicolo
  • 11 (literal)
Note
  • ISI Web of Science (WOS) (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#affiliazioni
  • 1) Institute of Intelligent Systems for Automation, National Research Council, Genova 16149, Italy; 2) Institute of Intelligent Systems for Automation, National Research Council, Genova 16149, Italy (literal)
Titolo
  • Local Linear Regression for Function Learning: An Analysis Based on Sample Discrepancy (literal)
Abstract
  • Local linear regression models, a kind of nonparametric structures that locally perform a linear estimation of the target function, are analyzed in the context of empirical risk minimization (ERM) for function learning. The analysis is carried out with emphasis on geometric properties of the available data. In particular, the discrepancy of the observation points used both to build the local regression models and compute the empirical risk is considered. This allows to treat indifferently the case in which the samples come from a random external source and the one in which the input space can be freely explored. Both consistency of the ERM procedure and approximating capabilities of the estimator are analyzed, proving conditions to ensure convergence. Since the theoretical analysis shows that the estimation improves as the discrepancy of the observation points becomes smaller, low-discrepancy sequences, a family of sampling methods commonly employed for efficient numerical integration, are also analyzed. Simulation results involving two different examples of function learning are provided. (literal)
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