Nonlinear Modeling

1 Neural Nets and Related Model Structures for Nonlinear System Identification.- 1.1 Introduction.- 1.2 Black-box Identification Approach.- 1.3 Fitting the Parameters.- 1.4 The Nonlinear Mapping.- 1.5 Some Standard Theory on Model Properties.- 1.6 Bias-Variance Trade-off.- 1.7 Discussion.- 1.8 Dynamic Systems.- 1.9 A stepwise Approach to Nonlinear Black-box Identification.- 1.10 Examples.- 1.11 Conclusions.- References.- 2 Enhanced Multi-Stream Kaiman Filter Training for Recurrent Networks.- 2.1 Introduction.- 2.2 Network Architecture and Execution.- 2.3 Gradient Calculation.- 2.4 EKF Multi-Stream Training.- 2.5 A Modeling Example.- 2.6 Alternating training of weights and initial states.- 2.7 Toward more coordinated training of weights and states-A Motivating Example.- 2.8 The Mackey-Glass Series.- 2.9 Use of a structured evolver.- 2.10 Summary.- References.- 3 The Support Vector Method of Function Estimation.- 3.1 Introduction.- 3.2 The Optimal Hyperplane.- 3.3 The Support Vector Machine for Pattern Recognition.- 3.4 Examples of SV Machines for Pattern Recognition.- 3.5 The SVM for regression estimation.- 3.6 Kernels for Estimating Real-Valued Functions.- 3.7 Solving Operator Equations.- 3.8 Conclusion.- References.- 4 Parametric Density Estimation for the Classification of Acoustic Feature Vectors in Speech Recognition.- 4.1 Introduction.- 4.2 The Probability Densities.- 4.3 Maximum Likelihood Estimation.- 4.4 Mixture Models.- 4.5 Numerical experiment.- 4.6 Conclusion.- References.- 5 Wavelet Based Modeling of Nonlinear Systems.- 5.1 Introduction.- 5.2 Wavelet Interpolation Method.- 5.3 Wavelet Interpolation in Sobolev Space.- 5.4 Numerical Examples.- 5.5 Conclusions.- Appendix: Constrained Minimal Norm Interpolation.- References.- 6 Nonlinear Identification based onFuzzy Models.- 6.1 Introduction.- 6.2 Functional fuzzy models.- 6.3 Fuzzy Modelling algorithms without structure determination.- 6.4 Structure determination.- 6.5 A worked example.- 6.6 Discussion.- References.- 7 Statistical Learning in Control and Matrix Theory.- 7.1 Introduction.- 7.2 Paradigm of Controller Synthesis Problem.- 7.3 Various Types of “Near” Minima.- 7.4 A General Approach to Randomized Algorithms.- 7.5 Some Sufficient Conditions for the UCEM Property.- 7.6 Robust Stabilization.- 7.7 Weighted H?Norm Minimization.- 7.8 Randomized Algorithms for Matrix Problems.- 7.9 Sample Complexity Issues.- 7.10 Conclusions.- References.- 8 Nonlinear Time-Series Analysis.- 8.1 Introduction.- 8.2 State space reconstruction.- 8.3 Influence of the reconstruction parameters.- 8.4 Noise reduction.- 8.5 Detecting nonlinearities.- 8.6 Modelling and prediction.- 8.7 Fractal dimensions.- 8.8 Lyapunov exponents.- 8.9 Synchronization of chaotic dynamics.- 8.10 Spatio-temporal time series.- References.- 9 The K.U.Leuven Time Series Prediction Competition.- 9.1 Introduction.- 9.2 Origin of the data.- 9.3 Results of the competition.- 9.4 Conclusions.- References.