URL study guide
https://tue.osiris-student.nl/onderwijscatalogus/extern/cursus?cursuscode=2AMU30&collegejaar=2025&taal=enDescription
This course introduces students to advanced theories of uncertainty that can be used in data science, artificial intelligence, and machine learning for representing and reasoning with knowledge. Concretely, it covers belief functions, possibility theory, fuzzy sets, credal sets, and general imprecise probability theories. These theories are ideal for enhancing our capabilities to provide robust and interpretable results. We treat various aspects: modelling principles, approaches for learning and reasoning, and the application to decision making. The theories shine when learning from relatively limited amounts of data or when robustness is required. So, the course discusses robust decision making for scenarios of high risk or with stringent safety requirements.
The course consists of lectures, exercises, and an assignment. The lectures mostly cover the theories, including small illustrations of derivations and calculations for inference and decision making. Those should be practiced more-in-depth with the provided exercises, where difficult cases are discussed in instructions (organized alongside regular lectures). The assignment, a literature study of a chosen application involving uncertainty, is meant to deepen the understanding of the theories. Its deliverables are a report and a presentation.
Assumed knowledge/prerequisites for this course are:
- Probability theory (essential); for example, as taught in 2DI90, JBM010, or 2DL70 (certainly: laws of probability, multivariate probability, marginal and conditional probability, Bayes’s rule, independence, random variables, probability mass functions, probability density functions)
- Statistics (desirable); for example, as taught in 2DI90, JBM010, 2WS20, or 2WS30 (certainly: concept of point and interval estimation)
- Linear algebra (essential); for example, as taught in 2DBI00 or 2WF20 (certainly: algebraic equations, vector, matrices)
- Calculus (essential); for example, as taught in 2DB03, 2WxB0, 2DL1x (certainly: integration)
- Logic & Set Theory (essential); for example, as taught in 2IT60 or 2IHT10 (certainly: set & logical operations, logic notation, Boolean algebra)
- Notions of optimization (desirable); for example, as taught in 2AMS50 or 2AMU10
Objectives
- Understand the principles of uncertainty representation and reasoning under uncertainty
- Apply inference and decision-making approaches based on uncertainty modeling theories such as probability theory, belief functions, and imprecise probabilities
- Describe the trade-offs between computational complexity and expressiveness required in the choice of model for uncertainty representation and the application of algorithms for inference and decision making
- Describe how one can model applications involving (a high degree of) uncertainty using various uncertainty representation theories
- Compare different uncertainty representation theories in terms of suitability for a specific application based on the nature(s) and degree(s) of uncertainty involved
- Write a coherent scientific text (literature study comparing theories) that is accessible to fellow students
- Present the conclusions of a scientific literature study in a way that is accessible to fellow students