Advanced Topics of Estimation and Optimization

Recommended Prerequisites

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

Teaching Methods

The weekly lessons are organized as follows:

1. Theoretical exposition and discussion:

a. 1 hour of preparation through previous readings of bibliographic material previously available;

b. 2 to 3 hours of study to consolidate knowledge;

2. 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, classification and learning.

Learning Outcomes

The skills to be acquired in this curricular unit refer to the knowledge of methods for estimation, classification, and learning, both from a theoretical and formal perspective, or from a practical perspective and from a computational development perspective. The objectives of the course are generally applied in all fields of engineering and computational sciences where it is necessary to make inference from data. The skills to be acquired in this curricular unit also include the knowledge and mastery of classical and conventional techniques, as well as the initial study of the most modern methods based on machine learning.

Work Placement(s)

No

Syllabus

1.Estimation problems in engineering and computer science.

2.Parametric estimation. Least Squares. Robust est. RANSAC, LMedS. Bootstrap and Monte Carlo. Maximum likelihood. The Crámer-Rao lower bound.

3.Sub-space methods and Total LS. Singular values, principal components, Moor-Penrose PI, generalized inverse, conditioning and regularization.

4.Gradient descent methods. Newton Method. Non linear LS (Gauss-Newton, Levenberg-Marquardt).

5.Convex Optimization. Convex sets and functions. Dual problem. Approximation and fitting. Unconstrained minimization and Equality constrained minimization.

6.Bayes Decision Theory. Likelihood and a priori prob.; cost functions, optimal decision, conjugate priors. MAP method and of minimum variance. Inference with missing data (EM algorithm).

7.Stochastic proc. est. Non-linear filtering. Particles and Kalman filters. 

Assessment Methods

Assessment
Project: 100.0%

Bibliography

1. Parameter Estimation and Inverse Problems (3rd edition), R. Aster, B. Borchers and C. Thurber. Academic Press, 2018.

2.  Pattern Classification. R. Duda, P. Hart and D. Stork. Wiley-Interscience; 2nd ed. (Nov 2012) . [Estimação não paramétrica]

3. Probability, Random Variables and Sthocastic Processes, A. Papoulis and S. Pillai. McGrawHill (4th ed. 2002). [Probabilidades e Estatística]

4. Robust Estimation and Testing. R. Staudte and S. Sheather. John Wiley & Sons (1990).

5. Tracking and Data Association: Y. Bar-Shalom, T. Fortmann 0000 Academic Press

6. Convex Optimization. Stephen Boyd and Lieven Vandenberghe, University of California, Los Angeles. Cambridge University Press, 2004.