# PhD Course: Combinatorial and Algebraic Statistics

**Time: **
Fri 2021-01-22 10.00

**Lecturer: **
Liam Solus and Kathlén Kohn

**Location: **
Zoom, meeting ID: 694 5440 6589

### Abstract

Combinatorial and algebraic statistics is an emerging field within the mathematical foundations of data science and artificial intelligence. Many of the modern techniques utilized in these fields aim to identify optimal models or discern useful properties of data-generating distributions that allow practitioners to make informed predictions. Such techniques often make assumptions about the data-generating distribution that have in turn lead to the careful study of statistical models whose important features are naturally represented via combinatorial and/or algebraic objects. Such objects commonly include directed acyclic graphs, convex polytopes, and/or special algebraic varieties. What can be said about the combinatorics and algebra of these objects arising from statistical models of interest? Can the combinatorics and algebra of these objects teach us useful things about their statistical models of origin? These are the types of questions that will be explored in this class. Topics to be discussed include hypothesis tests for contingency tables, Markov bases for hierarchical and network models, likelihood inference for discrete and Gaussian models, conditional independence models, graphical models, and connections to phylogenetics. Following this course, participants should find themselves familiar with the basic objects of study currently discussed at a typical workshop or seminar on combinatorial and algebraic statistics. More information on the course is available at the course website: https://people.kth.se/~solus/combinatorial-algebraic-statistics-VT21.html .