Causal Models
Course at the 6th Tsinghua Logic Summer School, 2026
Instructors: Bonan Zhao and Tadeg Quillien (University of Edinburgh)
Location: Jianhua Building A308
Time: 9:50-12:15, June 29th-July 3rd
Teaching assistants: Wenlong Zheng (zhengwl21 at mails dot tsinghua dot edu dot cn) and Xiangyuan Ji (xy-ji23 at mails dot tsinghua dot edu dot cn)
Course description
This course explores formal approaches to causal reasoning. We begin with an introduction to causal graphical models, examining how Causal Bayes Nets and Structural Causal Models can be used to represent and reason about causal structures. These lectures emphasize the formal distinction between ‘seeing’ and ‘doing’.
We then discuss more recent approaches that represent causal knowledge with structured programs. We examine probabilistic program induction as a framework for causal reasoning, treating the acquisition of causal knowledge as a search problem over program spaces. Drawing on formal methods including probabilistic context-free grammars (PCFGs), approximate Bayesian inference, and adaptor grammars, we explore how structured representations enable few-shot learning and generalization.
The course concludes with an introduction to counterfactual reasoning and some of its applications to reasoning about causal responsibility.
Pre-requisites: Basic probability theory; Propositional and first-order logic.
Course material
Day 1: introduction to causal models
Lecture slides 1 Lecture slides 2 Lecture slides 3
Day 2: inference and learning in causal models
Lecture slides 1 Lecture slides 2 Lecture slides 3
Day 3: program induction
Day 4: approximate inference
Day 5: counterfactuals, conclusion
Lecture slides 1 Lecture slides 2
Homework and exams
Each homework is worth 20% of the grade. The final exam is worth 40%.
Homework 1 Due Wednesday at 09:50. Homework 1 answers
Homework 2 Due Friday at 09:50. Homework 2 answers
Homework 3 Due Monday at 23:59. Homework 3 answers
Readings (optional)
Introductory
N. D. Goodman, J. B. Tenenbaum, and The ProbMods Contributors (2016). Probabilistic Models of Cognition (2nd ed.) https://probmods.org/ (especially chapters 1 to 5)
Pearl, J., & Mackenzie, D. (2018). The book of why: the new science of cause and effect. Basic books.
Pearl, J. (2018). Theoretical impediments to machine learning with seven sparks from the causal revolution. arXiv preprint arXiv:1801.04016.
Advanced
Pearl, J. (2009). Causality. Cambridge university press. (especially chapters 1,3,7)
Zhao, B., Lucas, C. G., & Bramley, N. R. (2024). A model of conceptual bootstrapping in human cognition. Nature Human Behaviour, 8(1), 125-136.
Quillien, T., & Lucas, C.G. (2023). Counterfactuals and the logic of causal selection. Psychological Review.