Webrelaunch 2020

Bayesian Inverse Problems with Connections to Machine Learning (Summer Semester 2024)

Lecture: Monday 14:00-15:30 20.30 0.16
Problem class: Tuesday 15:45-17:15 20.30 0.16
Lecturer, Problem classes Sebastian Krumscheid
Office hours: by appointment
Room 3.031 Kollegiengebäude Mathematik (20.30)
Email: sebastian.krumscheid@kit.edu

General information

The course offers an introduction to the subject of statistical inversion, where, in its most basic form, the goal is to study how to estimate model parameters from data. We will introduce mathematical concepts and computational tools for systematically treating these inverse problems in a Bayesian framework, including an assessment of how uncertainties affect the solution. In the first part of the course, we will study the Bayesian framework for finite-dimensional inverse problems. While the first part will introduce some machine-learning ideas already, the second part will address how machine learning is impacting, and has the potential to impact further on, the subject of inverse problems. In the final part of the course, we will generalize the Bayesian inverse problem theory to a Banach space setting and discuss sampling strategies for accessing the Bayesian posterior.

Course content

  • Bayesian Inverse Problems and Well-Posedness
  • Linear-Gaussian Setting
  • Optimization Perspective on Bayesian Inverse Problems
  • Gaussian Approximation
  • Markov Chain Monte Carlo
  • Blending Inverse Problems and Machine-Learning
  • Bayesian Inversion in Banach spaces

Other topics that may be addressed if time permits.


Course material as well as further details can be found on the course's ILIAS page.