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Compared to the adaptive RPEM algorithm in Cheung, 2004 and 2005, this batch RPEM need not assign the learning rate analogous to the Expectation-Maximization (EM) algorithm (Dempster et al., 1977), but still preserves the capability of automatic model selection. Further, the convergence speed of this batch RPEM is faster than the EM and the adaptive RPEM in general. 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