Estimation of the Sample Frechet Mean: A Convolutional Neural Network Approach

TL;DR

This paper introduces a convolutional neural network-based algorithm to efficiently estimate the sample Frechet mean of graph-valued data, addressing the need for advanced tools in graph statistics and machine learning.

Contribution

The paper presents a novel CNN-based approach for fast and reliable estimation of the sample Frechet mean in graph-valued datasets, improving computational efficiency.

Findings

Successfully recovers the sample Frechet mean in various random graph ensembles

Demonstrates reliability and accuracy of the CNN approach

Offers a scalable alternative to traditional methods for graph mean estimation

Abstract

This work addresses the rising demand for novel tools in statistical and machine learning for "graph-valued random variables" by proposing a fast algorithm to compute the sample Frechet mean, which replaces the concept of sample mean for graphs (or networks). We use convolutional neural networks to learn the morphology of the graphs in a set of graphs. Our experiments on several ensembles of random graphs demonstrate that our method can reliably recover the sample Frechet mean.