Two-sample Testing on Latent Distance Graphs With Unknown Link Functions

TL;DR

This paper introduces a new statistical test for comparing two latent distance graphs to determine if they share the same underlying latent positions, even with limited data, using spectral estimates and rank correlation.

Contribution

It presents a novel test procedure for latent distance graphs that is valid, consistent, and effective with small sample sizes, leveraging spectral methods and rank correlation.

Findings

Test has power with only one sample per population.

Can distinguish between different age groups in neural connectome data.

Can discriminate seizure from non-seizure events in brain recordings.

Abstract

We propose a valid and consistent test for the hypothesis that two latent distance random graphs on the same vertex set have the same generating latent positions, up to some unidentifiable similarity transformations. Our test statistic is based on first estimating the edge probabilities matrices by truncating the singular value decompositions of the averaged adjacency matrices in each population and then computing a Spearman rank correlation coefficient between these estimates. Experimental results on simulated data indicate that the test procedure has power even when there is only one sample from each population, provided that the number of vertices is not too small. Application on a dataset of neural connectome graphs showed that we can distinguish between scans from different age groups while application on a dataset of epileptogenic recordings showed that we can discriminate between seizure and non-seizure events.