Geometry of Gaussian graphical model for the cycle

  • Martin Vodicka (MPI MiS, Leipzig)
E1 05 (Leibniz-Saal)


In statistics, linear concentration model is given by the linear space of the symmetric matrices. Given the linear space L, there are two interesting numbers: The degree of variety $L^{-1}$, obtained by inverting all matrices in L and ML-degree of the model. It was shown that for general space L these two numbers are the same. However, this is not true for some specific spaces L. In this talk we will discuss such a case when L is the space for the Gaussian graphical model for the cycle. In this case these two numbers are different. We will focus on the degree of the variety $L^{-1}$ for which there is an explicit formula, conjectured by Sturmfels and Uhler, which we were able to prove. The proof is based on the intersection theory in the space of complete quadrics, intersection theory in Grassmannian and a lot of combinatorics.

Mirke Olschewski

MPI for Mathematics in the Sciences Contact via Mail

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