On the afternoon of December 22, 2020. Professor Stephane Robin from INRA gave an online report entitled “Tree-based mixture distributions: Applications in ecology and epidemiology”. Xiaoqiang Wang hosted this report, teachers and graduate students of our school attended this report online.

Professor introduced that graphical models provide a powerful framework to analyze the dependency structure relating a set of random variables. And recently, the inference of the structure of a graphical model has received a lot of attention, and one of the main issue is the exploration of the space of possible graphs, which cannot be carried in a naive manner because of combinatorial complexity. Spanning trees constitute a subset of graph, which fulfill the popular sparsity assumption. Still, the tree structure is a too restrictive assumption for most applications. However, the Matrix-Tree theorem enables to integrate over the set of all spanning tree at the cost of the calculation of a determinant, which allows considering a mixture of tree-shaped graphical models. In this talk, we will show how mixtures of tree-shapes graphical models can be used to infer the graphical model of a set of variables and the applications in ecology and epidemiology. From this talk teachers and students all obtained better understandings of this tree-shapes graphical models, and benefit a lot.

The successful holding of this report has strengthened atmosphere in researching probability theory in our school. and deepened the friendship and cooperation between the two sides.