Multiobjective analysis of chaotic dynamic systems with sparse learning machines

Sparse learning machines provide a viable framework for modeling chaotic time-series systems. A powerful state-space reconstruction methodology using both support vector machines (SVM) and relevance vector machines (RVM) within a multiobjective optimization framework is presented in this paper. The utility and practicality of the proposed approaches have been demonstrated on the time series of the Great Salt Lake (GSL) biweekly volumes from 1848 to 2004. A comparison of the two methods is made based on their predictive power and robustness. The reconstruction of the dynamics of the Great Salt Lake volume time series is attained using the most relevant feature subset of the training data. In this paper, efforts are also made to assess the uncertainty and robustness of the machines in learning and forecasting as a function of model structure, model parameters, and bootstrapping samples. The resulting model will normally have a structure, including parameterization, that suits the information content of the available data, and can be used to develop time series forecasts for multiple lead times ranging from two weeks to several months.