分野別セミナー

Maximum entropy–based hypothesis testing for network models transforms subgraph‑count constraints from a null (e.g., G(m, p) or ERGMs) into an entropy‑maximizing reweighting of i.i.d. graphs, with the resulting Lagrange multiplier used as the test statistic for goodness‑of‑fit and two‑sample tests.
The analysis draws on free‑energy ideas from statistical physics, Jaynes’ maximum entropy under constraints, nonlinear large deviations and graphon variational principles for dense graphs, Z‑estimator asymptotics, and Stein’s method for Poisson approximation of subgraph counts in the sparse regime.
Pre-requisites: I will briefly introduce the tools from various fields required in the paper. However, knowledge of undergraduate probability and statistical physics will be helpful.