Adaptive Estimation of Nonparametric Geometric Graphs

Understand

This article studies the recovery of graphons when they are convolution kernels on compact (symmetric) metric spaces.

• This case is of particular interest since it covers the situation where the probability of an edge depends only on some unknown nonparametric function of the distance between latent points, referred to as Nonparametric Geometric Graphs (NGG).
• In this setting, adaptive estimation of NGG is possible using a spectral procedure combined with a Goldenshluger-Lepski adaptation method.
• The latent spaces covered by our framework encompass (among others) compact symmetric spaces of rank one, namely real spheres and projective spaces.