Statistical Signal Processing and Statistical Learning

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 and algorithms of statistical learning, to know how to apply these methods and algorithms to real life problems and to be capable of researching in the area of statistical signal processing and statistical learning.

Random variables and random vectors. Multidimensional Gaussian distribution. Discrete random processes: definition, stationarity and ergodicity, autocorrelation and power spectral density. Parameter estimation: LS, MVUE, ML. 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. Statistical learning. Dimensionality reduction. Discriminative models. Perceptron. Linear regression. SVM. Neural networks. Deep neural networks. Generative models. Bayesian decision theory. Unimodal models. Markov chains. Mixture models: Gaussian mixture models. Hidden Markov models. Bayesian learning. Graphical models. Bayesian networks. Markov random fields. Factor graphs and belief propagation. Applications of the described methods and algorithms.

Lectures, self-learning, term projects, presentations, active participation in the lectures, consultations.

The exam includes a written or oral final exam from the course material listed in the course content and completion and presentation of a term paper/project on a subject mutually agreed by the student and the teacher.