IMT, Toulouse

November 6-8 2019

• Caronline Uhler (MIT). Mini Course.

Graphical models are used throughout the natural sciences, social sciences, and economics to model statistical relationships between variables of interest. When studying graphical models, polynomial equations and combinatorial constraints naturally arise and call for algebraic and combinatorial methods to advance the statistical methodology. This mini-course will take a geometric, algebraic and combinatorial perspective on graphical models. A main objective is to discuss identifiability in graphical models and develop methods for learning the graph and its parameters. Towards this end, we will highlight the role of conic duality for Gaussian graphical models and discuss the inherent combinatorial structures for causal structure discovery. The overarching goal of this course is to provide an overview of the interplay of techniques from algebra, combinatorics, and algebraic geometry, with problems arising in graphical models.