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Estimation and Classification
Post-Graduation in Electrical and Computers Engineering
Objective: this course addresses the following questions:
- how to compute variables which can not be directly measured by sensors ?
- how to obtain models for observed data (signals, images, video) and use these models in decision problems ?
These are fundamental questions in many electrical engineering areas such as robotics, vision, medical imaging, communications or pattern recognition.
Program
1. Introduction . Estimation problems in robotics, image processing,
artificial intelligence and multimedia. Inference and learning.
2. Parameter estimation. Least Squares Method. Robust estimation.
RANSAC algorithms.
3. Classic Estimation Theory . Maximum likelihood method.
Performance evaluation. The Cr�mer-Rao Bound.
4. Bayesian Inference. Conjugate priors. MAP and minimum variance methods.
Model order estimation.
5. Inference with unobserved variables: the EM method.
Estimation of multiple models.
6. Data classification. Discriminant functions. Bayesclassifier. Model learning.
Pattern Recognition applications.
7. Estimation of stochastic processes **.**�Stochastic dynamic models.
Nonlinear filtering. Particle filter. Kalman filter.
8. Hidden Markov models. Likelihood function. The forward-backward algorithm.
State sequence estimation. Viterbi algorithm. Model estimation.
9. Graphical models and Bayesian networks. Directed acyclic graphs. Joint distribution.
Independence conditions.� Inference methods. Junction Trees. Monte Carlo methods.
Forward backward algorithm in factor graphs.
Bibliography
I will provide every week the viewgraphs for each topic in the program. I am not aware of a single text book covering all the topics. The following references provide most of the information you need.
� Duda, Hart, Stork, Pattern Classification, Wiley, 2001. ((Topics: 2-6))
� Jorge S. Marques, Reconhecimento de Padr�es M�todos Estat�sticos e Neuronais, IST Press, 1999. (Topics: 2-6)
� Y. Bar Shalom, T. Fortmann, Tracking and Data Association, Academic Press (Topics: 7)
� F. Jensen, Bayesian Networks and Decision graphs, Springer-Verlag, 2001. (Topics: 9)
� L. Rabiner. A tutorial on hidden markov models and selected applications in speech recognition, Proceedings of the IEEE, 77(2):257-284, February 1989. (Topics: 8)