Schedule

Topics:

• Course overview, objectives, and logistics
• Foundations of statistical machine learning
• The roles of uncertainty in learning and decision-making
• Limitations and pitfalls of conventional learning paradigms
• Motivation for imprecise probabilistic machine learning

Suggested readings: TBA

Topics:

• Understanding uncertainty and probability
• Interpretations of probability
• Limitations of precise probability models (e.g., Ellsberg’s paradox)
• Motivation for imprecise probabilities
• Overview of imprecise probabilistic models: lower and upper previsions, sets of desirable gambles, credal sets, and related representations

Suggested readings:

• Imprecise Probabilities — Stanford Encyclopedia of Philosophy
• Interpretations of Probability — Stanford Encyclopedia of Philosophy

Topics:

• Gambles and their interpretation
• Sets of desirable gambles
• Lower prevision, linear prevision, and lower probabilities
• Coherence and avoiding sure loss
• Natural extension and coherent inference

Suggested readings: TBA

Topics:

• Historical background and motivation
• Possibility distributions
• Possibility and necessity measures
• Connections to imprecise probability
• Statistical properties and inference
• Applications in machine learning

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)

Topics:

• Historical background and motivation
• Belief functions and their interpretations
• Belief and plausibility measures
• Dempster’s rule of combination
• Connections to imprecise probability
• Applications in machine learning

Suggested readings:

• Decision-Making with Belief Functions: a Review by T. Denœux (2019)

Topics:

• Motivation: decision-making under uncertainty
• From Bayesianism to quasi-Bayesianism and infra-Bayesianism
• Convex sets of probability measures and their representations
• Connections to other imprecise probabilistic models, including lower previsions and sets of desirable gambles
• Learning and reasoning with credal sets, including notions of independence and conditional independence

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

Topics:

• Updating and conditioning rules for imprecise probabilities
• Decision making under imprecision
• Decision criteria: maximality, E-admissibility, Γ-maximin, Γ-maximax, interval dominance
• Dynamic consistency and sequential decision-making
• Robustness, dilation, and the value of information

Suggested readings:

• Decision Making under Uncertainty using Imprecise Probabilities by Matthias C. M. Troffaes
• SIPTA School 2024: Decisions by Matthias C. M. Troffaes

Topics:

• Classification and regression under imprecision
• Credal predictors and set-valued predictions
• Learning objectives, loss functions, and risk
• Calibration and evaluation of imprecise predictions
• Selective prediction, abstention, and indeterminate decisions

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)

Topics:

• Quantifying aleatoric and epistemic uncertainty
• Axiomatic characterization of uncertainty measures
• Uncertainty quantification for structured outputs beyond token-level predictions
• Evaluation and calibration of uncertainty estimates
• Applications in machine learning

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

Topics:

• From probabilistic to set-valued prediction
• Conformal prediction and finite-sample coverage guarantees
• Conformal prediction from an imprecise-probabilistic perspective
• Calibration of precise and imprecise probabilistic predictions
• Validity, efficiency, and informativeness of predictive sets
• Applications in machine learning

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

Topics:

• Simpson’s paradox and causal ambiguity
• Causal assumptions and identifiability
• Partial identification and causal bounds
• Imprecise probabilities for representing causal knowledge
• Robust inference and decision-making under causal uncertainty

Suggested readings: TBA

Topics:

• Sequential decision-making under imprecise uncertainty
• Imprecise Markov decision processes and robust reinforcement learning
• Exploration, abstention, and decision-making under epistemic uncertainty
• AI safety under distribution shift and model uncertainty
• Preference uncertainty, reward uncertainty, and AI alignment
• Multi-agent decision-making with imprecise beliefs

Suggested readings: TBA

Topics:

• Compositional generalisation and reasoning about unseen compositions
• Extrapolation under partial knowledge and underspecification
• Open-world and open-ended learning
• Novelty, ignorance, and the unknown
• Scientific discovery and hypothesis generation under epistemic uncertainty
• Metacognition and reasoning about the limits of knowledge

Suggested readings: TBA