Probabilistic Prediction of Chaotic Time Series Using Similarity of Attractors and LOOCV Predictable Horizons for Obtaining Plausible Predictions

This paper presents a method for probabilistic prediction of chaotic time series. So far, we have developed several model selection methods for chaotic time series prediction, but the methods cannot estimate the predictable horizon of predicted time series. Instead of using model selection methods employing the estimation of mean square prediction error (MSE), we present a method to obtain a probabilistic prediction which provides a prediction of time series and the estimation of predictable horizon. The method obtains a set of plausible predictions by means of using the similarity of attractors of training time series and the time series predicted by a number of learning machines with different parameter values, and then obtains a smaller set of more plausible predictions with longer predictable horizons estimated by LOOCV (leave-one-out cross-validation) method. The effectiveness and the properties of the present method are shown by means of analyzing the result of numerical experiments.22nd International Conference, ICONIP 2015, November 9-12, 2015, Istanbul, Turke

Performance improvement via bagging in probabilistic prediction of chaotic time series using similarity of attractors and LOOCV predictable horizon

Recently, we have presented a method of probabilistic prediction of chaotic time series. The method employs learning machines involving strong learners capable of making predictions with desirably long predictable horizons, where, however, usual ensemble mean for making representative prediction is not effective when there are predictions with shorter predictable horizons. Thus, the method selects a representative prediction from the predictions generated by a number of learning machines involving strong learners as follows: first, it obtains plausible predictions holding large similarity of attractors with the training time series and then selects the representative prediction with the largest predictable horizon estimated via LOOCV (leave-one-out cross-validation). The method is also capable of providing average and/or safe estimation of predictable horizon of the representative prediction. We have used CAN2s (competitive associative nets) for learning piecewise linear approximation of nonlinear function as strong learners in our previous study, and this paper employs bagging (bootstrap aggregating) to improve the performance, which enables us to analyze the validity and the effectiveness of the method

Hierarchical Clustering of Ensemble Prediction Using LOOCV Predictable Horizon for Chaotic Time Series

Recently, we have presented a method of ensemble prediction of chaotic time series. The method employs strong learners capable of making predictions with small error, where usual ensemble mean does not work well owing to the long term unpredictability of chaotic time series. Thus, we have developed a method to select a representative prediction from a set of plausible predictions by means of using LOOCV (leave-one-out cross-validation) measure to estimate predictable horizon. Although we have shown the effectiveness of the method, it sometimes fails to select the representative prediction with long predictable horizon. In order to cope with this problem, this paper presents a method to select multiple candidates of representative prediction by means of employing hierarchical K-means clustering with K = 2. From numerical experiments, we show the effectiveness of the method and an analysis of the property of LOOCV predictable horizon.The 2017 IEEE Symposium Series on Computational Intelligence (IEEE SSCI 2017), November 27 to December 1, 2017, Honolulu, Hawaii, US