Postgraduate Course: Targeted Causal Learning (MATH11238)
Course Outline
School  School of Mathematics 
College  College of Science and Engineering 
Credit level (Normal year taken)  SCQF Level 11 (Postgraduate) 
Availability  Not available to visiting students 
SCQF Credits  10 
ECTS Credits  5 
Summary  You might hear the statement: My headache went away because I took an aspirin. But was it really the aspirin? In everyday life, causal language is often used in an informal way. However, extracting precise answers to causal questions from data requires careful consideration. First, one should assess if the data, whether observational or generated by a designed randomised experiment, is rich enough to answer the causal question. Second, one should develop and use statistical techniques with mathematical guarantees to accurately estimate the quantity of interest.
In the first part of the course, we consider causal questions based on various data structures: From completely randomised experimental designs to various types of observational studies. We look at the role randomisation, design and confounding play in our ability to address these questions. For example, how should one design a population cohort, such as the Universitys Generation Scotland, to deal with confounding, maximise efficiency, and minimise bias in addressing national health policy? Causal questions, such as Did the aspirin cure my headache?, can be expressed using NeymanRubins theory of potential outcomes. Throughout, the material is illustrated by examples and case studies from fields such as biomedicine and healthcare policy, economics, and climate science.
In the second part of the course, we turn to a general estimation strategy to answer (causal) questions from observational data. In realworld applications, learning the datas ground truth distribution is often challenging or near impossible. At the same time, seemingly helpful simplifications may render estimates biased and statistical inference invalid. Rather than relying on parametric assumptions, we introduce a modelindependent approach to estimation called Targeted Learning (TL). TL integrates causal inference with machine learning, leading to valid statistical inference of (causal) quantities of interest, such as the average causal effect. The relevant statistical theory will be developed, and the methods will be applied to relevant examples and case studies using the available TL packages (tlverse) in R 
Course description 
In this course, we study causal inference from designed experiments and observational
data via targeted estimation. Topics may include:
 Designed experiments vs observational data, role of confounding
 Basics of causal inference, e.g., potential outcomes, matching
 Case study: Design of population cohorts
 Modelindependent definition of a statistical parameter,
 Ensemble learning and crossvalidation,
 Targeted Maximum Likelihood Estimation for statistical inference

Entry Requirements (not applicable to Visiting Students)
Prerequisites 
Students MUST have passed:
Statistical Computing (MATH10093) OR
Statistical Programming (MATH11176) OR
Machine Learning and Pattern Recognition (INFR11130) OR
Extended Statistical Programming (MATH11242)

Corequisites  
Prohibited Combinations  
Other requirements  Suggested course in parallel: Methods for Causal Inference (INFR11207)
It is REQUIRED that students have foundational understanding of probability and statistical methodology, and are familiar with programming in R, Python, or similar. R is the course language.
Note that PGT students on School of Mathematics MSc programmes are not required to have taken prerequisite courses, but they are advised to check that they have studied the material covered in the syllabus of each prerequisite course before enrolling. 
Course Delivery Information

Academic year 2024/25, Not available to visiting students (SS1)

Quota: None 
Course Start 
Semester 2 
Timetable 
Timetable 
Learning and Teaching activities (Further Info) 
Total Hours:
100
(
Lecture Hours 22,
Seminar/Tutorial Hours 5,
Summative Assessment Hours 2,
Programme Level Learning and Teaching Hours 2,
Directed Learning and Independent Learning Hours
69 )

Assessment (Further Info) 
Written Exam
80 %,
Coursework
20 %,
Practical Exam
0 %

Additional Information (Assessment) 
Coursework: 20%
Examination: 80% 
Feedback 
Not entered 
Exam Information 
Exam Diet 
Paper Name 
Hours & Minutes 

Main Exam Diet S2 (April/May)  Targeted Causal Learning (MATH11238)  2:00  
Learning Outcomes
On completion of this course, the student will be able to:
 Explain the nature of randomisation and the problem of confounding
 Recognise and apply various experimental designs
 Decide which methods to apply to extract causality from experimental and observational data
 Provide modelindependent definitions of (causal) quantities of interest and apply Ensemble Learning and crossvalidation estimation strategies
 Apply Targeted Maximum Likelihood Estimation to case studies

Reading List
Main textbooks:
 Lecture notes by the Course Organiser
 Imbens, G.W. and Rubin, D.B. (2015). Causal inference in statistics, social, and biomedical sciences. Cambridge University Press.
 Van der Laan, M.J. and Rose, S. (2011). Targeted Learning: Causal Inference
for Observational and Experimental Data. Springer, New York.
Further reading:
 Box, G.E.P. and Hunter, J.S. and Hunter, W.G. (2005). Statistics for experimenters: design, innovation and discovery. Wiley.
 Gelman, A. and Hill, J. and Vehtari, A. (2021). Regression and other stories. Cambridge University Press.
 Benkeser, D. and Chambaz, A. (2020). A Ride in Targeted Learning Territory. https://achambaz.github.io/tlride/
 Van der Laan, M.J. et al (2021). Targeted Learning in R: Causal Data Science with the tlverse Software Ecosystem. https://tlverse.org/tlversehandbook/ 
Additional Information
Graduate Attributes and Skills 
Not entered 
Keywords  TCL,Designed Experiments,Observational Data,Causal Inference,Targeted Learning,Modelindependent Est 
Contacts
Course organiser  Dr Sjoerd Viktor Beentjes
Tel:
Email: Sjoerd.Beentjes@ed.ac.uk 
Course secretary  Miss Kirstie Paterson
Tel:
Email: Kirstie.Paterson@ed.ac.uk 

