Reading Group In Algebraic Statistics

Organized by Eliana Duarte and Ben Hollering

Goals:

Algebraic Statistics studies and solves of problems in Statistical Data Analysis using tools from Algebraic Geometry, Commutative Algebra, Discrete Geometry and, numerical and symbolic computation. This is an active and exciting field of research that started almost three decades ago. The goal of this reading course is, in the first part, to establish a common language for statistics and algebra; in the second part we will focus on more advanced topics and current developments.

In the future months there will be many activities around Algebraic Statistics, these include the 3-Way-Interaction-Seminar, several Minisymposia at the SIAM AG23 Conference, and finally the semester long program Algebraic Statistics and Our Changing World at IMSI. Participants in this reading group will be set up for an enriched experience in attending any of the aforementioned events.

Format:

Each session is 90 minutes, split in two 35 minute blocks. Two people give talks which they prepare together. We meet at 1:30pm on Thursdays excep on April 20th we meet at 2pm. Starting April 6th

Dates:

1. April 6th, 2023. MPI-MIS. Room: G3-10. Algebra and Statistics Primer. Karel Devriendt, Javier Sendra - Ch.3 Algebra Primer, Ch.4. Conditional Independence, Ch.5 Statistics Primer
2. April 13th, 2023. MPI-MIS. Room: G3-10. Exponential Families a.k.a Toric Varieties. Leoni Kayser, Alexander Kreiss - Ch. 6 Exponential families a.k.a toric varieties
3. April 20th, 2023. E1 05 (Leibniz-Saal). Maximum Likelihood Geometry. Max Wiesmann, Dmitrii Pavlov - Ch.7 Likelihood Inference, Likelihood geometry, ML degree. We start at 2pm this day.
4. May 4th, 2023. MPI-MIS. Room: G3-10. Discrete Graphical Models. Tabea Krause, Lisa Seccia. Ch.13. Graphical Models
5. May 11th, 2023. MPI-MIS. Room: G3-10. Exercises - Questions- Clarification. The suggested exercises for this session are in this FILE.

Fundamentals:

From Sullivant’s Book available in pdf or hard copy at the MPI library.

• Ch.3 Algebra Primer ,Ch.4. Conditional Independence ,Ch.5 Statistics Primer
• Ch.6 Exponential Families, a.k.a Toric Varieties
• Ch.7 Likelihood Inference, Likelihood geometry, ML degree
• Ch.13 Graphical Models - Discrete
• Exercises, questions clarification.
• Ch.13 Graphical Models - Gaussian

More advanced topics

• Ch.15. Phylogenetics
• Ch.14. Hidden Variables, tensors, Mixture models
• Nonparametric Statistics
• Gaussian Likelihood Geometry of Projective Varities
• Complete quadrics: Schubert Calculus for Gaussian Models and Semidefinite Programming
• Likelihood equations and scattering amplitudes
• Marginal Independence Models

Aditional References

• Drton, Sturmfels, Sullivant, “Lectures in Algebraic Statistics”
• Maathuis, Drton, Lauritzen, Wainwright, “Handbook of Graphical models”
• Pachter and Sturmfels “Algebraic Statistics for Computational Biology”