Abstract
The curse of dimensionality has long been a hurdle in the analysis of complex data in areas such as computational biology, ecology and econometrics. In this work, we present a forecasting algorithm that exploits the dimensionality of data in a nonparametric autoregressive framework. The main idea is that the dynamics of a chaotic dynamical system consisting of multiple time-series can be reconstructed using a combination of different variables. This nonlinear autoregressive algorithm uses multivariate attractors reconstructed as the inputs of a neural network to predict the future. We show that our approach, attractor ranked radial basis function network (AR-RBFN) provides a better forecast than that obtained using other model-free approaches as well as univariate and multivariate autoregressive models using radial basis function networks. We demonstrate this for simulated ecosystem models and a mesocosm experiment. By taking advantage of dimensionality, we show that AR-RBFN overcomes the shortcomings of noisy and short time-series data.
Highlights
In a notable theorem, Takens proved that the overall behavior of a chaotic dynamic system can be reconstructed from lags of a single variable[17]
By merging the top manifolds and the information contained in them, attractor ranked radial basis function network (AR-radial basis function networks (RBFN)) is capable of recovering the dynamics of the system in a manner that outperforms model-free approaches such as multiview embedding (MVE) and nonlinear univariate and multivariate autoregressive models
To assess the performance of the AR-RBFN approach, we compare the forecast performance between the out-of-sample forecast estimates and the one-step-ahead observations using our proposed AR-RBFN autoregressive model with that of a model-free approach based on nearest neighbors, MVE, proposed by Ye et al.[20]
Summary
Takens proved that the overall behavior of a chaotic dynamic system can be reconstructed from lags of a single variable[17]. Takens’ theorem was later generalized and it was demonstrated that the information from a combination of multiple time-series (and their lags) can be used in an attractor reconstruction to provide a more mechanistic model[18,19]. Since attractor reconstruction relies only on experimental data, the limitations of short or noisy time-series restricts the ability to infer system dynamics as a whole. We treat prediction of the dynamical system as an inverse problem that involves interpolation and approximating an unknown function from a time-series data and introduce an attractor ranked radial basis function network (AR-RBFN)-based autoregressive model. By merging the top manifolds and the information contained in them, AR-RBFN is capable of recovering the dynamics of the system in a manner that outperforms model-free approaches such as MVE and nonlinear univariate and multivariate autoregressive models
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