Two-Sample Testing for Inhomogeneous Random Graphs in Non-Integral $L_r$ Norms
Testing whether two populations of networks share the same edge probabilities is a basic problem in network inference. How hard it is depends on the norm used to measure the difference. For the inhomogeneous Erdős--Rényi (IER) model, the optimal sample complexity is known for every integer $L_r$ norm and for $1\le r<2$. For non-integral $r>2$, however, the known upper and lower bounds do not match, and the lower bound was conjectured to be tight. We study this gap for two-sample testing on aligned vertices. We propose a test that runs two published statistics, of orders $2$ and $\lceil r\rceil$, on the same data and rejects if either one rejects. Its thresholds come from Hölder interpolat...
| Authors | Soham Dan |
|---|---|
| Primary category | stat.ML |
| Published | 27 September 2026 |
| Last updated at source | 27 September 2026 |
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