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.
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 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.
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 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)