FSF3960 Algebraic Statistics 7.5 credits
Content and learning outcomes
Course contents
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Probability Primer
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Algebra Primer
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Conditional Independence
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Statistics Primer
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Exponential Families
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Likelihood Inference
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The Cone of Sufficient Statistics
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Fisher's Exact Test
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Graphical Models
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Hidden Variables
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Identifiability
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Singular Learning Theory
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MAP Estimation
Intended learning outcomes
By the end of the course, the participants
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will be able to explain how statistical models for discrete random variables are relevant to (semi) algebraic varieties and ideals.
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will be able to deal use algebraic methods on 1) Independence models 2) CI (=conditional indepencence) models with hidden variables 3) CI axioms from algebraic point of view 4) Primary Decomposition of CI Ideals
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Apply algebraic methods to Exponential families, Sufficient statistics
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Apply geometry of CI
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Compute the algebraic invariants of the ideals associated to discrete models.
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Use matrix Schubert varieties in Gaussian conditional independence models
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Solve a maximal likelihood estimation of an implicit model with algebraic methods
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Deal with identifiability and singularity issues in models with algebraic tools.
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know the open problems in this developing field.
Literature and preparations
Specific prerequisites
Masters degree in mathematics, or in computational mathematics or in computer science/engineering with at least 30 cu in mathematics and 20 cu in statistics.
Suitable prerequisites are courses: SF2935 Modern Methods of Statistical Learning and SF2737 Commutative Algebra and Algebraic Geometry
Recommended prerequisites
Equipment
Literature
Algebraic Statistics by Seth Sullivant. (Available as a preprint)
Lectures on Algebraic Statistics by Mathias Drton, Bernd Sturmfels and Seth Sullivant.
Oberwolfach Seminars Volume 39, 2008, Springer Science \& BusinAess Media
Examination and completion
If the course is discontinued, students may request to be examined during the following two academic years.
Grading scale
Examination
Based on recommendation from KTH’s coordinator for disabilities, the examiner will decide how to adapt an examination for students with documented disability.
The examiner may apply another examination format when re-examining individual students.
Home assignments and computer work
Other requirements for final grade
The examination is computer project P/F and homework assignments (80 % correct).
Opportunity to complete the requirements via supplementary examination
Opportunity to raise an approved grade via renewed examination
Examiner
Ethical approach
- All members of a group are responsible for the group's work.
- In any assessment, every student shall honestly disclose any help received and sources used.
- In an oral assessment, every student shall be able to present and answer questions about the entire assignment and solution.