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    | Titel | An experiment on the evolution of an ensemble of neural networks for streamflow forecasting |  
    | VerfasserIn | M.-A. Boucher, J.-P. Laliberté, F. Anctil |  
    | Medientyp | Artikel 
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    | Sprache | Englisch 
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    | ISSN | 1027-5606 
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    | Digitales Dokument | URL |  
    | Erschienen | In: Hydrology and Earth System Sciences ; 14, no. 3 ; Nr. 14, no. 3 (2010-03-30), S.603-612 |  
    | Datensatznummer | 250012232 
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    | Publikation (Nr.) |  copernicus.org/hess-14-603-2010.pdf |  
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        | Zusammenfassung |  
        | We present an experiment on fifty multilayer perceptrons trained for
      streamflow forecasting on three watersheds using bootstrapped input series. This type of neural network
      is common in hydrology and using multiple training repetitions
      (ensembling) is a popular practice: the information issued by the
      ensemble is then aggregated and considered to be the final
      output. Some authors proposed that the ensemble could serve the
      calculation of confidence intervals around the ensemble mean. In the
      following, we are interested in the reliability of confidence
      intervals obtained in such fashion and in tracking the evolution of
      the ensemble of neural networks during the training process. For each
      iteration of this process, the mean of the ensemble is computed along
      with various confidence intervals. The performance of the ensemble
      mean is evaluated based on the mean absolute error. Since the ensemble
      of neural networks resemble an ensemble streamflow forecast, we also
      use ensemble-specific quality assessment tools such as the Continuous
      Ranked Probability Score to quantify the forecasting performance of
      the ensemble formed by the neural networks repetitions. We show that
      while the performance of the single predictor formed by the ensemble
      mean improves throughout the training process, the reliability of the
      associated confidence intervals starts to decrease shortly after the
      initiation of this process. While there is no moment during the
      training where the reliability of the confidence intervals is
      perfect, we show that it is best after approximately 5 to 10
      iterations, depending on the basin. We also show that the Continuous
      Ranked Probability Score and the logarithmic score do not evolve in
      the same fashion during the training, due to a particularity of the
      logarithmic score. |  
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