Postgraduate Course: Methods for Causal Inference (INFR11207)
Course Outline
School  School of Informatics 
College  College of Science and Engineering 
Credit level (Normal year taken)  SCQF Level 11 (Postgraduate) 
Availability  Available to all students 
SCQF Credits  10 
ECTS Credits  5 
Summary  Causal inference is an important emerging area in AI and data science allowing us to move away from merely associational statements towards causeeffect statements. Being able to develop and/or apply causal inference techniques has broad applications in social and biomedical sciences, e.g., in answering questions such as "How effective is a given treatment for curing/preventing a disease?" or "Which genetic variants can causally increase the risk of disease and hence be targeted by drugs?" or "What economic policy could have prevented the 2008 financial crisis?"
In this course we develop causal inference techniques to address the above questions. This is a relatively advanced course and students are expected to be familiar with foundations of probability, statistics and calculus (see "Other Requirements" box) 
Course description 
The aims and the structure of the course are as follows:
 Estimating causal effects: Why correlations alone are misleading?
 Randomised trials vs observational data
 Part I: Causal Effect Estimation
 Rubin's framework: Potential outcomes with observed and unobserved confounders
 Pearl's framework: Structural causal models with observed and unobserved confounders
 Computer simulations and numerical exercises in Python
 Part II: Causal Discovery
 Constraintbased algorithms and Scorebased algorithms
 Functional Causal Models
 Computer simulations and numerical exercises in Python
Teaching of the theory is followed by illustrative examples from biomedicine and social sciences, together with appropriate computer simulations and numerical exercise.

Entry Requirements (not applicable to Visiting Students)
Prerequisites 
It is RECOMMENDED that students have passed
Machine Learning and Pattern Recognition (INFR11130) AND
Probability (MATH08066)

Corequisites  It is RECOMMENDED that students also take
Probabilistic Modelling and Reasoning (INFR11134)

Prohibited Combinations  
Other requirements  This course is open to all MSc students at School of Informatics, including those on joint degrees. The course is also available to MSc students at School of Mathematics (e.g. MSc Statistics and Data Science).
Required prerequisite: Students should have passed MLPR (INFR11130) or Probability (MATH08066) or an equivalent course indicating facility with probabilistic models and mathematical thinking.
Maths requirements:
1. Linear algebra: Vectors, matrices: addition, multiplication, inversion, diagonalization (eigenvectors).
2. Special functions: properties and combination rules for logarithm and exponential.
3. Calculus: Differentiation and integration.
4. Probability theory: Discrete and continuous univariate random variables. Expectation, variance. Univariate Gaussian distribution. Joint and conditional distributions.
Programming requirements:
Students should be familiar with programming in a modern objectoriented language, ideally Python which is the course language. 
Information for Visiting Students
Prerequisites  Same as "other requirements". 
High Demand Course? 
Yes 
Course Delivery Information

Academic year 2021/22, Available to all students (SV1)

Quota: None 
Course Start 
Semester 2 
Timetable 
Timetable 
Learning and Teaching activities (Further Info) 
Total Hours:
100
(
Lecture Hours 20,
Seminar/Tutorial Hours 5,
Summative Assessment Hours 2,
Revision Session Hours 2,
Programme Level Learning and Teaching Hours 2,
Directed Learning and Independent Learning Hours
69 )

Additional Information (Learning and Teaching) 
Feedback on asignments are provided during the lectures and tutorials

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

Feedback 
 Questions on material during the lectures will be discussed
 Two feedback sessions within lecture hours, after each of the two course assignments (one formative, one summative)
 Feedback on the work during tutorials
 Weekly online quiz on Learn, with solutions provided after answering the questions (not assessed)
 Course forum on Learn for students to ask questions 
Exam Information 
Exam Diet 
Paper Name 
Hours & Minutes 

Main Exam Diet S2 (April/May)  Methods for Causal Inference (INFR11207)  2:00  
Learning Outcomes
On completion of this course, the student will be able to:
 Explain the difference between causal and associational estimation and justify why causal inference techniques are necessary to derive meaning from observational data
 Explain the difference between randomised trials vs observational studies related to public health and other types of data more generally
 Learn and apply foundational causal estimation techniques using two major frameworks: (i) Rubin's Potential Outcomes and (ii) Pearls Structural (graphical) causal models to simulated examples and real world data, in the presence of observed and unobserved variables
 Explain different types of causal discovery algorithm, learn their underlying assumptions and shortcomings, and be able to apply them to data using available software.
 Be able to modify/repurpose a current technique in order to apply it to a particular problem of interest.

Reading List
Books that may be useful but not required:
1) Causal Inference in Statistics: A Primer (Pearl, Glymour, Jewell, 2016).
2) Elements of Causal Inference: Foundations and Learning Algorithms (by Peters, Janzing and Schölkopf
3) More advanced: Causality (Pearl, 2009) 
Additional Information
Graduate Attributes and Skills 
problemsolving, critical/analytical thinking, independent learning, crosscultural or crossdisciplinary communication 
Keywords  Causal inference,causal discovery,data science,probability and statistics,Machine Learning,MCI 
Contacts
Course organiser  Dr Ava Khamseh
Tel: (0131 6)51 1426
Email: Ava.khamseh@igmm.ed.ac.uk 
Course secretary  Ms Lindsay Seal
Tel: (0131 6)50 2701
Email: lindsay.seal@ed.ac.uk 

