Extended Kalman Filter Based Echo State Network for Time Series Prediction using MapReduce Framework

Echo state networks (ESNs), that exhibit good performance for modeling a nonlinear or non-Gaussian dynamic system, have been widely used for time series prediction. However, estimating the output weights of the ESNs remains intractable. Extended Kalman filter (EKF) is an effective estimate method, but its computational cost is relatively high. In this study, a MapReduce framework based parallelized EKF is proposed to learn the parameters of the network, in which two MapReduce based models are designed, and each of them is composed of a set of mapper and reducer functions. The mapper receives a training sample and generates the updates of the internal states or the output weights, while the reducer merges all updates associated with the same key to produce an average value. To verify the effectiveness and the efficiency of the proposed method, an industrial data prediction problem coming from the blast furnace gas (BFG) system in steel industry is employed for the validation experiments, and the experimental results demonstrate that the proposed parallelized EKF can efficiently estimate the parameters of the ESN with good performance and computing time.