Computational Techniques of Detection, Estimation and Identification
Advanced Computational Methods
2nd Cycle Studies - Mestrado
Algebra, Calculus, Probabilities and Statistics, Computer Programming (C and Matlab)
1. Theoretical exposition and discussion (~25% of the time):
a. 1h preparation - previous readings of bibliographic material;
b. 2 to 3h of consolidation study;
2. Laboratory lessons (~75% of the time):
a. 2 to 3h of consolidation study;
b. Monitoring of the final projects.
The evaluation consists in the elaboration and presentation of a final project related to an individual theme to accord with the teachers. It is expected that the project (in a publishable format) analyses a set of data to direct application of one or more techniques for estimation, detection and/or identification.
The present course focuses on computational methods for estimation, detection and identification. The subjects taught in this class have a broad range of application in almost all domains of engineering and computer science. We will learn how to infer information from data. The first part focuses on estimation assuming an implicit parametric model. On the second part we will overview some stochastic estimation techniques as well as non-parametric estimation. In the third part, we will focus the fundamentals of new and modern techniques involving machine learning.
1. Parameter Estimation
a. Direct and Inverse problems
b. Mathematic models
c. Linear and non-linear inverse problems
2. Linear Regression
a. Least square problems (LS)
b. Maximum likelihood solutions
c. Error propagation
3. Robust Estimation
a. Statistical bias and normalization
b. Unknown statistical error distribution
c. Bootstarp and Monte-Carlo
d. Outliers, RANSAC and LMedS
4. Subspace methods and Total LS
a. SVD decomposition
b. Principal components
c. Moore-Penrose pseudo-inverse
d. Generalized inverse
e. Conditioning problems and truncated singular values
g. Total and Generalized LS
5. Non-linear Optimization
a. Convex objective functions and local extrema
b. Local and global minima. Annealing techniques and convergence issues
c. Constrained and unconstrained optimization
6. Stochastic estimation methods
7. Non parametric estimation
8. Fundamentals of estimation, detection and identification using machine learning
Nuno Miguel Mendonça da Silva Gonçalves
1. Numerical Recipes in C++, W. Press, S. Teukolsky, W. Vetterling and B. Flannery. 3rd ed. (2007), Cambridge University Press.
2. Parameter Estimation and Inverse Problems (2nd edition), R. Aster, B. Borchers and C. Thurber. Academic Press, Jan 2012.
3. Convex Optimization, S. Boyd and L. Vandeberghe. Cambridge University Press (Mar 2004). [Optimização Convexa]
4. Numerical Methods for Unconstrained Optimization and Nonlinear Equations, J. Dennis and R. Schnabel. SIAM Classics in Applied Mathmatics (1996). [Optimização não linear]
5. Pattern Classification. R. Duda, P. Hart and D. Stork. Wiley-Interscience; 2nd ed. (Nov 2000) . [Estimação não paramétrica]
6. Practical Methods of Optimization. R. Fletcher. Wiley (May 2000). [Optimização Não Linear]
7. Probability, Random Variables and Sthocastic Processes, A. Papoulis and S. Pillai. McGrawHill (4th ed. 2002). [Probabilidades e Estatística]
8. Robust Estimation and Testing. R. Staudte and S. Sheather. John Wiley & Sons (1990).