Mathematical methods in signal processing and machine learning. I. Linear signal representation and approximation: Hilbert spaces, LMMSE estimation, regularization and sparsity. II. Learning linear and nonlinear functions and filters: neural networks, kernel methods. III. Structured statistical models: hidden Markov models, factor graphs, Kalman filter, Gaussian models with sparse events.
Lernziel
The course is an introduction to some basic topics in signal processing and machine learning.
Inhalt
Part I - Linear Signal Representation and Approximation: Hilbert spaces, least squares and LMMSE estimation, projection and estimation by linear filtering, learning linear functions and filters, L2 regularization, L1 regularization and sparsity, singular-value decomposition and pseudo-inverse, principal-components analysis. Part II - Learning Nonlinear Functions: fundamentals of learning, neural networks, kernel methods. Part III - Structured Statistical Models and Message Passing Algorithms: hidden Markov models, factor graphs, Gaussian message passing, Kalman filter and recursive least squares, Monte Carlo methods, parameter estimation, expectation maximization, linear Gaussian models with sparse events.
Skript
Lecture notes.
Voraussetzungen / Besonderes
Prerequisites: - local bachelors: course "Discrete-Time and Statistical Signal Processing" (5. Sem.) - others: solid basics in linear algebra and probability theory
Leistungskontrolle
Information zur Leistungskontrolle (gültig bis die Lerneinheit neu gelesen wird)
Leistungskontrolle als Semesterkurs