Algebraic geometry with a view towards applications
- Eliana Duarte (MPI MiS, Leipzig + Otto von Guericke University Magdeburg)
Computational algebraic geometry offers a concrete approach to study systems of polynomial equations in several variables. This is useful in several applications in engineering and data science. In this talk we focus on its application in Statistics to study graphical models. We study these models using combinatorics, toric geometry and algebra. Our results provide a more general framework, using staged tree models, to understand the defining equations of widely known graphical models such as decomposable models and discrete Bayesian networks.