Course notes / topics
This page keeps track of course notes, material covered, homework schedule, and other relevant links. Unlike the static course homepage, this one is updated weekly.
- Most lectures use slides in the beginning, but I always also write on the board to supplement examples.
- It is impossible to follow the course only by reading these slides; students are expected to attend the lectures as well.
- All course communication, updates, announcements, logistics, and grading takes place on our Canvas course page.
Week 1 - invitation to algebraic statistics
Homework 1 assigned. due 1/27/2026
Week 2 - statistical models, independence, and notation
Week 3 - algebraic varieties (what polynomials define), and basic computations
Week 4 - Statistics primer intro to MLE
- lecture 7
- including related book readings here
- MLE for the model of independence of 2 random variables
- Student (Solomon) finishes the previous lecture by presenting the MLE for the independence model of 2 random variables.
notes
Homework 2 assigned. due 2/19/2026
Week 5
Week 6
What are ideals used for, actually? And examples to complete last week.
Week 7
Exact testing for discrete exponential families.
Week 8
- On the first day, we discussed your solutions to Homework set 2!
- On the second day, we defined Markov bases, discussed the Fundamental Theorem, some basic implications, and some examples of computing from Worksheets & homework.
lecture 14
Homework 3 assigned. due 3/24/2026
Week 9
- In-class worksheet 4, finish at home. I should have posted this last week!
Are there any other issues with contingency tables we need to worry about?
- Cell bounds and disclosure limitation, lecture 15
- Sampling bounds and structural zeros
Homework 4 assigned. due 4/2/2026
- Hidden variable models. We discussed the hidden variables, their meaning, their use, and algebraic/geometric interpretation. We basically went over these lecture notes. You may find the following student presentation from KTH also very insightful extra notes; see page 3!
Week 10
Welcome back from Spring Break week! :)
We are staring to discuss graphical models!
- Background and notation, global/local/pairwise Markov properties. For lecture17, we covered the undirected models from the PDF notes – the first 7 pages. Please also see the material from lecture 17, part 2
- lecture 18: we covered Gaussianp[lecture18-graphicalModels-Gaussian.pdf] graphical models (the main statement is that non-edges of the graph correspond to the zeros of the concentration matrix; see book!)
- Then we went over section 2.2 in these same notes from lect17: why do we need directed graphical models? and the definitions of the 3 directed Markov properties (pairwise, local, global).
Homework 5 assigned. due 4/14/2026
Homework 6 assigned. due 5/4/2026 Early submission most welcome!
Week 11
- 3/31 lecture 19: parametrization of graphical models.
- 4/2(at Simons; online check-ins; time for project work)
Week 12
Project presentations begin!
- 4/7 Priscilla Ama Yinzime: “Uncovering proximity of chromozome territories using classical algebraic staitstics”
- 4/9 Nishanth Srinivas Gurjar
Week 13
- 4/14 Megan Millet: “Algebra Primer & Model Selection Examples”
- 4/16 Minjung Kang
Week 14
Week 15
- 4/28 Gbenga Solomon
- 4/30 Tawfiq Abusara
Final exams week
Monday May 4th - time slot as needed (10:30am-12:30pm)
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Appendix
What is this page?
Math 561 is a graduate-level course on algebraic and geometric methods in statistics. Course homepage is here, containing detailed info on the material, grading, etc.
Useful Info
Sample files: how to create your first .Rmd file! All of your HW can be submitted using markdown and html/pdf. Here are some templates I created for another course, just so you know what to expect:
Types of files
- html - course handouts.
- PDF - slides for short illustrations used within a live lecture
- Rmd - raw R Markdown code. This has two purposes:
1) for students to see how the basic output files are generated, and
2) to enable collaborators to make updates to the materials in future semesters.