On the afternoon of December 22, 2020, Stéphane Robin,  Senior Researcher at Institut National de la Recherche Agronomique (France) gave an online report entitled ”Tree-based mixture distributions: Applications in Ecology and Epidemiology”. Director of statistics department, Wang Xiaoqiang presided over this talk. Faculty members Zhou Li, Yang Fengkai, Qi Xingqin and graduate students attended this online meeting.

Probabilistic Graphical Models are a combination of probability theory and graph theory, which can reveal the interdependent structure of a set of random variables. Probabilistic Graphical Models is a trending research field of statistical learning currently, and it has a wide range of applications in many fields. In this talk, Stéphane Robin started with two practical problems, how to construct the interaction network of species and how to model the spread of epidemics, and gradually moved on to probabilistic graphical models and Tree-based mixture distributions. In the first half of the report, Stéphane Robin mainly introduced how mixtures of tree-shaped graphical models can be used to infer the graphical model of a set of variables. He thinks that the tree-shaped assumption is too restrictive for most applications. However, tree-shaped regarded as random variables, the Matrix-Tree theorem enables to integrate over the set of all spanning tree at the cost of the calculation of a determinant, which means that the graphical structure of the variables can be inferred. In the second part, Stéphane Robin presented two applications based on mixture of tree-shaped graphical models: the construction of the species interaction network in community ecology and the inference of spread path of an epidemic in epidemiology. And Stéphane Robin shared the problems encountered by their team during the study and the research in the future, and answered questions patiently. This report introduced the new research of the probabilistic graphical models, which broadened the horizons of the participants, and it was instructive to the further research.

Author: Mengxue Li, School of Mathematics and Statistics