SYSTEM IDENTIFICATION AND DATA ANALYSIS

1. Review of classical Statistical theory;
2. Linear models estimation: Maximum Likelihood, vector and matrix least squares problems
3. Conditioning and regularization. Ridge regression, the Lasso and related algorithms. Basic Spline regression.
4. Linear Hypotheses and Linear Discriminant Analysis. Pattern recognition, the Perceptron and the basic ideas of Support Vector Machines
5. Bayesian Statistics, MAP and minimum variance estimation. The Hilbert space setting.
6. Principal Components Analysis (PCA), data compression and applications to recognition and classification problems. The continuous parameter case: Reproducing Kernels.
7. Non linear Inference: Neural Networks and logistic regression
8. Basics on stationary random processes. Modeling and identification of Time Series; parameter estimation of ARX models and their asymptotic behaviour. The problem of order selection.
9. Recursive identification algorithms. Kalman filter like algorithms.