2021/05/30 by Daniel Ferguson, Ferguson, Daniel, François G. Meyer +2
Computer Science · Mathematics · Physics and Astronomy · #Advanced Graph Neural Networks #Applications (stat.AP) #Combinatorics (math.CO) #Complex Network Analysis Techniques #Data Analysis #FOS: Computer and information sciences #FOS: Mathematics #FOS: Physical sciences #Graph theory and applications #Machine Learning (stat.ML) #Social and Information Networks (cs.SI) #Statistics and Probability (physics.data-an) #cs.SI #math.CO #physics.data-an #stat.AP #stat.ML
paper · pdf · doi:10.48550/arxiv.2105.14397
14 pages
openalex publication_date 2021/05/30 · arxiv created 2022/01/16 · arxiv updated 2022/01/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The availability of large datasets composed of graphs creates an unprecedented need to invent novel tools in statistical learning for graph-valued random variables. To characterize the average of a sample of graphs, one can compute the sample Frechet mean and median graphs. In this paper, we address the following foundational question: does a mean or median graph inherit the structural properties of the graphs in the sample? An important graph property is the edge density; we establish that edge density is an hereditary property, which can be transmitted from a graph sample to its sample Frechet mean or median graphs, irrespective of the method used to estimate the mean or the median. Because of the prominence of the Frechet mean in graph-valued machine learning, this novel theoretical result has some significant practical consequences.