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DRPS : Course Catalogue : School of Mathematics : Mathematics

Postgraduate Course: Targeted Causal Learning (MATH11238)

Course Outline
SchoolSchool of Mathematics CollegeCollege of Science and Engineering
Credit level (Normal year taken)SCQF Level 11 (Postgraduate) AvailabilityAvailable to all students
SCQF Credits10 ECTS Credits5
SummaryYou 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 Neyman-Rubins 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 real-world 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 model-independent 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
- Model-independent definition of a statistical parameter,
- Ensemble learning and cross-validation,
- Targeted Maximum Likelihood Estimation for statistical inference
Entry Requirements (not applicable to Visiting Students)
Pre-requisites Students MUST have passed: Statistical Computing (MATH10093) OR Statistical Programming (MATH11176) OR Machine Learning and Pattern Recognition (INFR11130)
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.
Information for Visiting Students
High Demand Course? Yes
Course Delivery Information
Academic year 2023/24, Available to all students (SV1) 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:
  1. Explain the nature of randomisation and the problem of confounding
  2. Recognise and apply various experimental designs
  3. Decide which methods to apply to extract causality from experimental and observational data
  4. Provide model-independent definitions of (causal) quantities of interest and apply Ensemble Learning and cross-validation estimation strategies
  5. 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.
- Van der Laan, M.J. et al (2021). Targeted Learning in R: Causal Data Science with the tlverse Software Ecosystem.
Additional Information
Graduate Attributes and Skills Not entered
KeywordsTCL,Designed Experiments,Observational Data,Causal Inference,Targeted Learning,Model-independent Est
Course organiserDr Sjoerd Viktor Beentjes
Course secretaryMiss Gemma Aitchison
Tel: (0131 6)50 9268
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