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FSF3960 Algebraic Statistics 7.5 credits

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Information per course offering

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Course syllabus as PDF

Please note: all information from the Course syllabus is available on this page in an accessible format.

Course syllabus FSF3960 (Autumn 2009–)
Headings with content from the Course syllabus FSF3960 (Autumn 2009–) are denoted with an asterisk ( )

Content and learning outcomes

Course contents

  1. Probability Primer

  2. Algebra Primer

  3. Conditional Independence

  4. Statistics Primer

  5. Exponential Families 

  6. Likelihood Inference

  7. The Cone of Sufficient Statistics

  8. Fisher's Exact Test

  9. Graphical Models

  10. Hidden Variables  

  11. Identifiability

  12. Singular Learning Theory

  13. MAP Estimation

Intended learning outcomes

By the end of the course, the participants

  • will be able to explain how  statistical models for discrete random variables  are relevant to (semi) algebraic varieties and ideals.  

  • 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

  • Apply algebraic methods  to Exponential families, Sufficient statistics

  • Apply  geometry of CI

  • Compute the algebraic invariants of the ideals associated to discrete models.

  • Use matrix Schubert varieties  in  Gaussian conditional independence models     

  • Solve a maximal likelihood estimation of an implicit model with algebraic methods

  • Deal with   identifiability and singularity  issues in models    with algebraic tools.

  • 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

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

Grading scale

G

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.

    If the course is discontinued, students may request to be examined during the following two academic years.

    Home assignments and computer work

    Other requirements for final grade

    The examination is  computer project  P/F and  homework assignments (80 % correct).

    Examiner

    Profile picture Timo Koski

    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.

    Further information

    Course room in Canvas

    Registered students find further information about the implementation of the course in the course room in Canvas. A link to the course room can be found under the tab Studies in the Personal menu at the start of the course.

    Offered by

    SCI/Mathematics

    Education cycle

    Third cycle

    Postgraduate course

    Postgraduate courses at SCI/Mathematics