Chaotic time series prediction based on a novel robust echo state network

Decai Li, Min Han, Jun Wang

Research output: Contribution to journalArticlepeer-review

234 Citations (Scopus)


In this paper, a robust recurrent neural network is presented in a Bayesian framework based on echo state mechanisms. Since the new model is capable of handling outliers in the training data set, it is termed as a robust echo state network (RESN). The RESN inherits the basic idea of ESN learning in a Bayesian framework, but replaces the commonly used Gaussian distribution with a Laplace one, which is more robust to outliers, as the likelihood function of the model output. Moreover, the training of the RESN is facilitated by employing a bound optimization algorithm, based on which, a proper surrogate function is derived and the Laplace likelihood function is approximated by a Gaussian one, while remaining robust to outliers. It leads to an efficient method for estimating model parameters, which can be solved by using a Bayesian evidence procedure in a fully autonomous way. Experimental results show that the proposed method is robust in the presence of outliers and is superior to existing methods.

Original languageEnglish
Article number6177672
Pages (from-to)787-797
Number of pages11
JournalIEEE Transactions on Neural Networks and Learning Systems
Issue number5
Publication statusPublished - 2012
Externally publishedYes


  • Echo state network (ESN)
  • Laplace likelihood function
  • robust model
  • surrogate function


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