# 227-0427-00L Signal Analysis, Models, and Machine Learning

Semester | Autumn Semester 2019 |

Lecturers | H.‑A. Loeliger |

Periodicity | yearly recurring course |

Language of instruction | English |

Abstract | 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. |

Objective | The course is an introduction to some basic topics in signal processing and machine learning. |

Content | 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. |

Lecture notes | Lecture notes. |

Prerequisites / Notice | Prerequisites: - local bachelors: course "Discrete-Time and Statistical Signal Processing" (5. Sem.) - others: solid basics in linear algebra and probability theory |