# 227-0427-00L Signal and Information Processing: Modeling, Filtering, Learning

Semester | Autumn Semester 2016 |

Lecturers | H.‑A. Loeliger |

Periodicity | yearly recurring course |

Language of instruction | English |

Abstract | Fundamentals in signal processing, detection/estimation, and machine learning. I. Linear signal representation and approximation: Hilbert spaces, LMMSE estimation, regularization and sparsity. II. Learning linear and nonlinear functions and filters: kernel methods, neural networks. III. Structured statistical models: hidden Markov models, factor graphs, Kalman filter, parameter estimation. |

Objective | The course is an introduction to some basic topics in signal processing, detection/estimation theory, 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 maximisation, sparse Bayesian learning. |

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 |