A neural network architecture, which models synapses as Finite Impulse Response (FIR) linear filters, is discussed for use in time series prediction. Analysis and methodology are detailed in the context of the Santa Fe Institute Time Series Prediction Competition. Results of the competition show that the FIR network performed remarkably well on a chaotic laser intensity time series. 1 Introduction The goal of time series prediction or forecasting can be stated succinctly as follows: given a sequence y(1); y(2); : : : y(N) up to time N , find the continuation y(N + 1); y(N + 2)::: The series may arise from the sampling of a continuous time system, and be either stochastic or deterministic in origin. The standard prediction approach involves constructing an underlying model which gives rise to the observed sequence. In the oldest and most studied method, which dates back to Yule [1], a linear autoregression (AR) is fit to the data: y(k) = T X n=1 a(n)y(k \Gamma n) + e(k) = y(k) + ...

A neural network architecture, which models synapses as Finite Impulse Response (FIR) linear filters, is discussed for use in time series prediction. Analysis and methodology are detailed in the context of the Santa Fe Institute Time Series Prediction Competition. Results of the competition show that the FIR network performed remarkably well on a chaotic laser intensity time series. 1 Introduction The goal of time series prediction or forecasting can be stated succinctly as follows: given a sequence y(1); y(2); : : : y(N) up to time N , find the continuation y(N + 1); y(N + 2)::: The series may arise from the sampling of a continuous time system, and be either stochastic or deterministic in origin. The standard prediction approach involves constructing an underlying model which gives rise to the observed sequence. In the oldest and most studied method, which dates back to Yule [1], a linear autoregression (AR) is fit to the data: y(k) = T X n=1 a(n)y(k \Gamma n) + e(k) = y(k) + e...

Abstract. Temporal pattern learning, control and prediction, and chaotic data analysis share a common problem: deducing optimal equations of motion from observations of time-dependent behavior. Each desires to obtain models of the physical world from limited information. We describe a method to reconstruct the deterministic portion of the equations of motion directly from a data series. These equations of motion represent a vast reduction of a chaotic data set’s observed complexity to a compact, algorithmic specification. This approach employs an informational measure of model optimality to guide searching through the space of dynamical systems. As corollary results, we indicate how to estimate the minimum embedding dimension, extrinsic noise level, metric entropy, and Lyapunov spectrum. Numerical and experimental applications demonstrate the method’s feasibility and limitations. Extensions to estimating parametrized families of dynamical systems from bifurcation data and to spatial pattern evolution are presented. Applications to predicting chaotic data and the design of forecasting, learning, and control systems, are discussed. 1.

Computational mechanics, an approach to structural complexity, defines a process’s causal states and gives a procedure for finding them. We show that the causal-state representation—an E-machine—is the minimal one consistent with

Data recorded in EEG based Brain-Computer Interface experiments is generally very noisy, non-stationary and contaminated with artifacts, that can deteriorate discrimination/classification methods. In this work we extend the Common Spatial Pattern (CSP) algorithm with the aim to alleviate these adverse effects. In particular we suggest an extension of CSP to the state space, which utilizes the method of time delay embedding. As we will show, this allows for individually tuned frequency filters at each electrode position and thus yields an improved and more robust machine learning procedure. The advantages of the proposed method over the original CSP method are verified in terms of an improved information transfer rate (bits per trial) on a set of EEG-recordings from experiments of imagined limb movements.

In recent years approximation theory has found interesting applications in the elds of Arti cial Intelligence and Computer Science. For instance, a problem that ts very naturally in the framework of approximation theory is the problem of learning to perform a particular task from a set of examples. The examples are sparse data points in a

This paper presents a tuturial introduction to predictions of stock time series. The various approaches of technical and fundamental analysis is presented and the prediction problem is formulated as a special case of inductive learning. The problems with performance evaluation of near-random-walk processes are illustrated with examples together with guidelines for avoiding the risk of data-snooping. The connections to concepts like "the bias-variance dilemma", overtraining and model complexity are further covered. Existing benchmarks and testing metrics are surveyed and some new measures are introduced.

The computer program pret automatically constructs mathematical models of physical systems. A critical part of this task is automating the processing of sensor data. pret's intelligent data analyzer uses geometric reasoning to infer qualitative information from quantitative data; if critical variables are either unknown or cannot be measured, it uses delay-coordinate embedding to reconstruct the internal dynamics from the external sensor measurements. Successful modeling results for two sensor-equipped systems, a driven pendulum and a radio-controlled car, demonstrate the effectiveness of these techniques.

Modeling pattern data series with cellular automata fails for a wide range of deterministic nonlinear spatial processes. If the latter have finite spatially-local memory, reconstructed cellular automata with infinite radius may be required. In some cases, even this is not adequate: an irreducible stochasticity remains on the shortest time scales. The underlying problem is illustrated and quantitatively analyzed using an alternative model class called cellular transducers. Contents List of Figures ........................................... iii Section 1

In this chapter, I review the main methods and techniques of complex systems science. As a