Lectures

Planned lecture topics for this offering. Slides are uploaded before each class; until then, the corresponding slides from the 2025/26 offering give an impression of the material.

• Lecture 1: Introduction
  tl;dr: The fundamentals of statistical machine learning, how uncertainty arises through data, models and environments, and why the limits of today's methods are rooted in probability theory.
  Slides: TBA
  

  Suggested readings: TBA

• Lecture 2: Overview of Imprecise Probability
  tl;dr: What uncertainty is and how probability is used to model it: interpretations of probability, aleatoric versus epistemic uncertainty, the limits of classical probability, and lower and upper previsions.
  Slides: TBA
  

  Suggested readings:

  • Imprecise Probabilities — Stanford Encyclopedia of Philosophy
  • Interpretations of Probability — Stanford Encyclopedia of Philosophy
• Lecture 3: Possibility Theory
  tl;dr: Possibility theory as a close relative of probability: basic belief assignments, possibility and necessity values, comparative possibility, and how to learn possibility models from data or expert input.
  Slides: TBA
  

  Suggested readings:

  • Possibility Theory and Statistical Reasoning by Didier Dubois (2006)
  • Possibility Theory and its Applications: Where Do we Stand? by Didier Dubois and Henri Prade (2014)
  • Possibilistic Inferential Models: A Review by Ryan Martin (2025)
• Lecture 4: Belief Function Theory
  tl;dr: Belief function theory, which generalises both probability and possibility: belief and plausibility measures, Choquet integration, Dempster's rule, and applications in machine learning.
  Slides: TBA
  

  Suggested readings:

  • Decision-Making with Belief Functions: a Review by T. Denœux (2019)
• Lecture 5: Convex Sets of Probabilities
  tl;dr: Credal sets as a unifying framework: characterisations, envelope functions, marginal and conditional credal sets, robust Bayesian inference, the Generalised Bayes Rule, and notions of independence.
  Slides: TBA
  

  Suggested readings:

  • Introduction to the Theory of Sets of Probabilities by Fabio Cozman
  • Introduction to the Theory of Imprecise Probability by Erik Quaeghebeur
  • SIPTA School 2024: Introduction to Imprecise Probabilities by Erik Quaeghebeur
• Lecture 6: Decision Making under Imprecision
  tl;dr: Decision making when probabilities are uncertain or incomplete: maximality, E-admissibility, Gamma-maximin and interval dominance, and their role in safer machine learning.
  Slides: TBA
  

  Suggested readings:

  • Decision Making under Uncertainty using Imprecise Probabilities by Matthias C. M. Troffaes
  • SIPTA School 2024: Decisions by Matthias C. M. Troffaes
• Lecture 7: Imprecise Classification and Regression
  tl;dr: How imprecise probability addresses overconfidence, adversarial vulnerability and lack of robustness in classification and regression, with concrete models extended by imprecise probability.
  Slides: TBA
  

  Suggested readings:

  • The Naïve Credal Classifier by Marco Zaffalon
  • Statistical modeling under partial identification by Georg Schollmeyer and Thomas Augustin (IJAR 2015)
  • Neural network model for imprecise regression with interval dependent variables by Krasymyr Tretiak, Georg Schollmeyer and Scott Ferson (Neural Networks 2023)
• Lecture 8: Uncertainty Quantification
  tl;dr: Why uncertainty quantification matters, how to distinguish and measure aleatoric, epistemic and total uncertainty, and the limitations of existing approaches.
  Slides: TBA
  

  Suggested readings:

  • Aleatoric and epistemic uncertainty in machine learning: an introduction to concepts and methods by Eyke Hüllermeier and Willem Waegeman
  • Quantification of Credal Uncertainty in Machine Learning by Eyke Hüllermeier, Sébastien Destercke and Mohammad Hossein Shaker
  • Integral Imprecise Probability Metrics by Siu Lun (Alan) Chau, Michele Caprio and Krikamol Muandet
• Lecture 9: Conformal Prediction and Calibration
  tl;dr: Conformal prediction as a distribution-free framework for uncertainty quantification, its connection to calibration and imprecise probability, and its use in trustworthy machine learning.
  Slides: TBA
  

  Suggested readings:

  • A Gentle Introduction to Conformal Prediction and Distribution-Free Uncertainty Quantification by Anastasios N. Angelopoulos and Stephen Bates
  • A Tutorial on Conformal Prediction by Glenn Shafer and Vladimir Vovk
• Lecture 10: Reflections, Open Problems, and Outlook
  tl;dr: Imprecise probability in deep learning, foundation models, LLMs and generative AI, and whether it can help with fairness, privacy, ethics and safety.
  Slides: TBA
  
• Lecture 11: Project and Use Case Presentations
  tl;dr: Students present their course projects and use cases.
  Slides: TBA