Year: 2020
Type: preprint
Abstract: We consider a latent space model for random graphs where a node $i$ is associated to a random latent point $X_i$ on the Euclidean unit ball. The probability that an edge exists between two nodes is determined by a ``link'' function, which corresponds to a dot product kernel. For a given class $\F$ of spherically symmetric distributions for $X_i$, we consider two estimation problems: latent norm recovery and latent Gram matrix estimation. We construct an estimator for the latent norms based on the degree of the nodes of an observed graph in the case of the model where the edge probability is given by $f(\langle X_i,X_j\rangle)=\mathbbm{1}_{\langle X_i,X_j\rangle\geq τ}$, where $0
Source: arXiv (Cornell University)
Author: Valdivia, Ernesto Araya
Institutions: Université Paris-Saclay, Laboratoire de Mathématiques d'Orsay
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W3094514062