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.
| 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] |
Christian | |
| 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] |
Fatemeh | |
| 30.4. | Intro Convexity & Optimization Polytopes, occur as marginal polytopes of statistical models, convex hull pb, Legendre duality, faces | [] [] |
Martin | |
| 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] |
Anna-Lena | |
| 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]) |
Laura | |
| 21.5. | Graphical Models ... as log-linear models, marginal polytopes, trees, chordal graphs, junction tree, treewidth | [AHT Ch.8] [GMS], [L Ch.4] |
Han | |
| 11.6. | Structure & Symmetry of Markov Bases | [AHT Ch.7 (Ch.5)] |
Julian | |
| 11.6. | No-3-Way-Interaction No-3-way-interaction model, facet complexity, Markov complexity | [AHT Ch.9] [EFRS] |
Daniele | |
| 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. |
| [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) |