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Seminar in Statistics: Causal Inference with Observational Data

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Seminar in Statistics:

Causal Inference with Observational Data

Sara van de Geer and Jonas Peters

§ 1 Concepts relating Graphs and Distribution

I Standard Concepts of Graphical Models (25.02.2013, J. Peters) Patrick Gasser, Florin Gegenschatz, Patrick Helbling

d-separation, conditional independences, Markov condition: Lauritzen (ask Jonas for details)

IIa Structural Equation Models and Counterfactuals (04.03.2013, J. Peters) Andrea Riva

Pearl: Chapter 1.4

IIb Faithfulness and Causal Minimality (04.03.2013, J. Peters) Steve Muller, Anja Franceschetti

Zhang and Spirtes: “Detection of Unfaithfulness and Robust Causal Inference”, Minds

& Machines (2008) 18:239-271, p. 239–252 top

Steel: “Homogeneity, selection, and the faithfulness condition”, Minds & Machines (2006) 16:303-317,

§ 2 Interventional Distributions

III Do-Statements and Simpson’s Paradox: (11.03.2013, C. Nowzohour) Andreas Puccio, Nadine Bachmann, Martin Davtyan

Pearl: Chapter 3.1, 3.2. (in particular 3.2.3), Chapter 6.1

IV Do-Calculus with Unobserved Variables (18.03.2013, C. Nowzohour) Colin James Stoneking, Fabio Ghielmetti, Lukas Benedikt Herrmann Pearl: Chapter 3.3, Backdoor and Frontdoor Criteria.

§ 3 Identifiability of Graphs

V Constraint-Based Methods (25.03.2013, C. Nowzohour) Gian-Andrea Peter Thanei, Andreas Luca Elsener, Zhou Syang

Markov Equivalence Class main result from Verma and Pearl: “Equivalence and Syn- thesis of Causal Models”, not Chapter 3.

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VI Restricted Structural Equation Models (08.04.2013, J. Peters) Ioan Gabriel Bucur, Timurs Butenko

(1) Linear Non-Gaussian Models: Darmois-Skitovic theorem and proof for two variables (ask Jonas for pdf), statement for p variables from (lingam), (optional: directLingam, probably not enough time)

(2) Linear Gaussian Models with Same Error Variances: Proof for two variables, state- ment from Peters and B¨uhlmann: “Identifiability of Gaussian Structural Equation Mod- els with Same Error Variances”, arXiv 2012, without proof.

§ 4 Identifying Graphs (Methods)

VII Constraint-Based Methods (22.04.2013, C. Nowzohour) Tobia Fasciati, Marco Felix Eigenmann, Shu Li

(1) PC algorithm, Spirtes et al: “Causation, Prediction and Search”, 5.1-5.4 (2) Partial Correlation as a test for conditional independence (without proofs) VIII Non-parametric Independence Test (29.04.2013, J. Peters)

Clara Valeria Pelloni, Ambra Barbara Toletti, Daniel Bruce MacKinlay

Gretton et al: “A Kernel Statistical Test of Independence”, NIPS 2007 (HSIC). Maybe better reference: Diploma thesis 3.1 and 3.3

IX Score-Based Methods with MEC search (06.05.2013, C. Nowzohour) Christina Heinze, Annette Aigner, David Josef B¨urge

Likelihood with same error variances or non-same error variances. Then description of greedy DAG search and greedy equivalence search. Chickering: “Optimal Structure Identification With Greedy Search”, JMLR 2002, 507-554

X Bayesian Methods (13.05.2013, J. Peters)

Jens Hauser, Caroline Anna Sophie Matthis, Anastasia Sycheva

Heckerman, Meek and Cooper: “A Bayesian Approach to Causal Discovery” Technical Report, MSR-TR-97-05, February 1997

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