Statistical Signal Processing and Statistical Learning

Course: Statistical Signal Processing and Statistical Learning

Code: 3ФЕИТ10031

ECTS points: 6 ECTS

Number of classes per week: 3+0+0+3

Lecturer: Prof. Dr. Venceslav Kafedjiski

Course Goals (acquired competencies): Upon completing the course it is expected that the student will understand and know how to implement the methods and algorithms of statistical signal processing: estimation of parameters, random parameters and random processes, and the methods of statistical learning, to know how to apply these methods and algorithms to real problems and to be capable of researching in the area of statistical signal processing and statistical learning.

Course Syllabus: Random variables and random vectors. Multidimensional Gaussian distribution. Discrete random processes: definition, stationarity and ergodicity, autocorrelation and power spectral density. Parameter estimation: MVUE, ML, LS. Estimation of random parameters: MAP, MMSE, and orthogonality principle. Optimal estimation of discrete random processes: Wiener and Kalman filter. Parametric models of discrete random processes: AR, MA and ARMA. Spectral analysis of discrete random processes: basic methods and high resolution methods. Adaptive signal processing. Array signal processing. Statistiscal learning. Linear regression. Classification. Linear discrimination. Bayesian classification. Kernel methods - SVM. Dimensionality reduction. Unsupervised learning. Neural networks. Deep neural networks. Graphical models. Bayesian networks.  Factor graphs and belief propagation. Models with latent variables. Discrete Markov models. Hidden Markov models (HMM). Learning of model parameters (EM and MCMC). Learning of model structure. Sparse signals and compressive sampling. Applications of the described methods and algorithms.

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