2020/10/26 by Ernesto Araya Valdivia, Valdivia, Ernesto Araya · 1 citation
Computer Science · Mathematics · #FOS: Computer and information sciences #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Markov Chains and Monte Carlo Methods #Point processes and geometric inequalities #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2010.13734
openalex publication_date 2020/10/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider a latent space model for random graphs where a node i is associated to a random latent point Xi 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 Xi, 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(⟨ Xi,Xj⟩)=\mathbbm1⟨ Xi,Xj⟩≥ τ, where 0