Objective: this course addresses the following questions:
These are fundamental questions in many electrical engineering areas such as robotics, vision, medical imaging, communications or pattern recognition.
1. Introduction. Estimation problems in robotics, image processing,
artificial intelligence and multimedia. Inference and learning.
2. Parameter estimation. Least Squares Method. Robust estimation.
3. Classic Estimation Theory. Maximum likelihood method.
Performance evaluation. The Crámer-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. Bayes classifier. Model learning.
Pattern Recognition applications.
7. Estimation of stochastic processes. Stochastic dynamic models.
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.
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 Padrões Métodos Estatísticos 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)