Computational Techniques for Estimation, Detection and Identification

Recommended Prerequisites

Algebra, Calculus, Probabilities and Statistics, Computer Programming (C and Matlab).

Teaching Methods

This course is taught in face-to-face lessons and evaluation is done continuously.
For that, the weekly lesson of 1 hour are organized as follows:
1.    Theoretical exposition and discussion:
a.    1 hour of preparation through previous readings of bibliographic material previously available in the Inforestudante platform;
b.    2 to 3 hours of study to consolidate knowledge;
2.    Monitoring of the final projects.

Learning Outcomes

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, and depending on the available time, we will overview some stochastic estimation techniques as well as non-parametric estimation.

Work Placement(s)

No

Syllabus

1. Introduction to parametric estimation

2. Linear regression
2.1 Linear least squares and its relation with maximum likelyhood estimation
2.2 Uncertainty propagation and confidence intervals
2.3 Tests of Q-Qplot and Chi-Square

3. Robust estimation
3.1 Statistical bias, equalization, and normalization
3.2 Errors with unknown statistics: Bootstrap and Monte-Carlo
3.3 RANSAC and LMedS for handling “outliers”
3.4 Minimization in L1 e Linf norms

4. Subspace methods and total least squares
4.1 SVD and PCA
4.2 Regularization
4.3 Total and generalized least squares
 
5. Introduction to non-linear estimation
5.1 Objective function, convexity, local extrema, singularities, and saddle points
5.2 Starting point, convergence issues, and annealing techniques
5.3 Optimization with no constraints
5.3.1 Newton Method
5.3.2 Non-linear least squares: Gauss-Newston e Levenberg-Marquadt
5.4 Optimization with constraints: Lagrange multipliers

Head Lecturer(s)

Nuno Miguel Mendonça da Silva Gonçalves

Assessment Methods

Assessment
The evaluation consists in the elaboration and presentation of a final project (100% of the final grade) 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: 100.0%

Bibliography

1. Numerical Recipes in C++, W. Press, S. Teukolsky, W. Vetterling and B. Flannery

2. Parameter Estimation and Inverse Problems, R. Aster, b. Borchers and C. Thurber

3. Convex Optimization (Livro avançado de Optimização Convexa), S. Boyd and L. Vandeberghe

4. Numerical Methods for Unconstrained Optimization and Nonlinear Equations

(Leitura complementar sobre optimização não linear), J. Dennis and R. Schnabel.

5.  Pattern Classification (Estimação não paramétrica). R. Duda, P. Hart and D. Stork.

6. Practical Methods of Optimization (Leitura complementar sobre Optimização Não Linear) R. Fletcher

7. Probability, Random Variables and Sthocastic Processes (Apoio sobre Probabilidades e Estatística), A. Papoulis and S. Pillai

8. Robust Estimation and Testing. R. Staudte and S. Sheather