Statistical comparison of graph-structured data and its application to distribution shift detection


Seminar Données et Aléatoire Théorie & Applications

25/05/2023 - 14:00 Etienne Lasalle (Université Paris-Saclay) Salle 106

When working with weighted graphs, one can interpret weights as the thermal conductivity of edges. Given initial conditions, one can use the way heat diffuses to compare graphs. Choosing relevant and informative diffusion times is often essential and challenging. To circumvent this issue, we choose to take into account the whole diffusion process. We define real-valued processes indexed by [0, T] for some T > 0, representing the comparisons for all diffusion times. Using tools from topological data analysis, we are able to compare graphs with unknown node correspondence or even graphs with different sizes.
In this talk, I will introduce these processes and present their statistical properties. From these results, we will see how we can construct consistent two-sample tests. Then I will present some applications to the detection of distribution shifts in the context of neural networks by using activation graphs.