Teaching Estimation and Control via Probabilistic Graphical Models – An Intuitive and Problem-Based Approach

Abstract

This contribution discusses an approach to teaching estimation and control via probabilistic graphical models, more specifically via Forney-style factor graphs, combined with a problem-based learning exercise model. The course's overall rationale follows the idea that factor graphs present a unifying perspective on a vast range of topics in estimation and control and may thus present a substantially more intuitive access to the subject matter. Factor graphs allow for a rigorous approach to algorithm design via mixing and matching graphical representations of algorithms or parts thereof. Even though there is a substantial overhead in explaining and understanding the way algorithms can be presented on graphical models via message passing, we postulate that this additional effort pays off by highlighting similarities, enabling easier modifications, and presenting a seamless framework combining approaches from classical control and modern machine learning. Accordingly, the course is set up to combine two goals: It (i) presents canonical topics, such as advanced Kalman filtering, parameter estimation and control, while (ii) simultaneously preparing students to continue research in the domain of probabilistic inference. To promote the latter, the exercises associated with the course adopt a problem-based learning approach, asking students to utilize and possibly extend a toolbox for factor graphs when attempting to solve relevant and mostly application-driven challenges.