Efficient Analysis of Latent Spaces in Heterogeneous Networks

TL;DR

This paper introduces a unified, efficient framework for latent space estimation in heterogeneous networks, enabling accurate decomposition of shared and network-specific components with theoretical error guarantees.

Contribution

It presents a novel procedure for identifying shared latent vectors and refining estimates using efficient score equations, achieving statistical efficiency and flexibility.

Findings

Oracle error rates for latent vector estimation are established.

The framework accommodates various edge weight distributions.

The method improves estimation accuracy in heterogeneous network models.

Abstract

This work proposes a unified framework for efficient estimation under latent space modeling of heterogeneous networks. We consider a class of latent space models that decompose latent vectors into shared and network-specific components across networks. We develop a novel procedure that first identifies the shared latent vectors and further refines estimates through efficient score equations to achieve statistical efficiency. Oracle error rates for estimating the shared and heterogeneous latent vectors are established simultaneously. The analysis framework offers remarkable flexibility, accommodating various types of edge weights under general distributions.