PREDICTING THE FUTURE: A CONNECTIONIST APPROACH

TLDR

The study investigates the effectiveness of connectionist architectures for predicting future behavior of nonlinear dynamical systems. The authors apply connectionist networks to short, noisy real‑world time series—sunspot data and a computational ecosystem—using validation and weight‑elimination to mitigate overfitting while extracting dynamical dimensions, Lyapunov coefficients, and nonlinearity. Sigmoid units outperform radial basis functions in high‑dimensional spaces, and sigmoid networks trained with weight‑elimination surpass traditional nonlinear statistical methods in prediction accuracy.

Abstract

We investigate the effectiveness of connectionist architectures for predicting the future behavior of nonlinear dynamical systems. We focus on real-world time series of limited record length. Two examples are analyzed: the benchmark sunspot series and chaotic data from a computational ecosystem. The problem of overfitting, particularly serious for short records of noisy data, is addressed both by using the statistical method of validation and by adding a complexity term to the cost function ("back-propagation with weight-elimination"). The dimension of the dynamics underlying the time series, its Liapunov coefficient, and its nonlinearity can be determined via the network. We also show why sigmoid units are superior in performance to radial basis functions for high-dimensional input spaces. Furthermore, since the ultimate goal is accuracy in the prediction, we find that sigmoid networks trained with the weight-elimination algorithm outperform traditional nonlinear statistical approaches.