Algebraic Statistics --- A Seminar

Summer 2015
Flyer [PDF]

every other Thursday, from 10 to 2
in SR 130, A3 (Hinterhaus)

Christian Haase
Martin Henk
Fatemeh Mohammadi

Algebraic statistics is a relatively new field full of exciting new developments. It combines questions and techniques from stochastics with those from (computational) algebraic geometry as well as convexity and polyhedral combinatorics.

If you are interested, please send us an email.

The Talks

date subject, keywords references speaker
16.4. Intro Stats
Sampler of problems: hypothesis testing for contingency tables, likelihood, MLE, sequence alignment? Sampler of models: independence ... conditional independence, hierarchical models, log-linear models, hidden variables?
 [DSS Ch.1.1]
[ASCB Ch.1]
16.4. Intro Algebra
Variety - ideal correspondence, prime ideals, primary decomposition, Groebner bases, examples from stats
 [CLO 1.4, 2.2, 2.3, 4.3-7]
[AHT Ch.3] [DSS], [ASCB]
30.4. Intro Convexity & Optimization
Polytopes, occur as marginal polytopes of statistical models, convex hull pb, Legendre duality, faces
30.4. Markov Bases
Fisher exact test, contingency table sampling, generalization to general Markov/Groebner/Graver-bases. Proof of fibers connected iff ideal generated
 [DSS Ch.1.2,1.3]
[AHT Ch.4], [J Ch.8], [dLHK]
21.5. Conditional Independence
Conditional statements, graphical models, parametrizations of graphical models, Markov properties, factorizations Hammersley-Clifford
 [L Ch 3.1, 3.2]
([DSS Ch.3] [J Ch.2,16])
21.5. Graphical Models
... as log-linear models, marginal polytopes, trees, chordal graphs, junction tree, treewidth
 [AHT Ch.8]
[GMS], [L Ch.4]
11.6. Structure & Symmetry of Markov Bases
 [AHT Ch.7 (Ch.5)]
11.6. No-3-Way-Interaction
No-3-way-interaction model, facet complexity, Markov complexity
 [AHT Ch.9]
25.6. Linear Concentration Models
Gaussian distributions, concentration matrix, convex and algebraic geometry of MLE
 [SU] ([U]) Carlos
25.6. Gaussian Graphical Models
 [U] ([SU]) Kathlén
16.7. Message Passing Algorithms
Cumulant function & its dual, marginalisation
 [WJ, Ch. 2.5,2.6] Yuanchen
16.7. Message Passing & Marginal Polytopes

First References

[DSS] Drton, Sturmfels and Sullivant
Lectures on Algebraic Statistics
Birkhäuser Basel. Series: Oberwolfach Seminars, Vol. 39 (2009)
[PS] Pachter and Sturmfels, eds.
Algebraic Statistics for Computational Biology
Cambridge University Press, New York (2005)
[WJ] Wainwright and Jordan (2008)
Graphical Models, Exponential Families, and Variational Inference
Foundations and Trends in Machine Learning Vol. 1, Nos. 1-2. 1-305 (2008)

[AHT] Aoki, Hara, Takemura
[CLO] Cox, Little, O'Shea
[dLHK] De Loera, Hemmecke, Köppe
[DSS] Drton, Sturmfels, Sullivant
[HS] Huh, Sturmfels
[J] Jordan
[L] Lauritzen
[ASCB] Pachter, Sturmfels
[WJ] Wainwright, Jordan
[GMS] Geiger, Meek, Sturmfels
[SU] Sturmfels, Uhler
[U] Uhler
[EFRS] Eriksson, Fienberg, Rinaldo, Sullivant