This talk by CSH scientist Samuel Martin-Gutierrez will take place on October 22, 2021 at 3PM (CET) in a hybrid format.
If you would like to attend, please send an email to email@example.com.
Title: “Network (co)variance. Networks of knowledge and other applications”
The variance of a probability distribution is a fundamental concept in the toolkit of probability theory and statistics and is routinely applied throughout science, engineering and numerous settings. In many practical cases however, probability distributions are defined on the nodes of a network. As the usual definition of variance cannot incorporate the network topology into the computation, we lack a basic methodological tool when analyzing distributions on networks. To bridge this methodological gap, we have developed a theory to measure the variance and covariance of probability distributions defined on the nodes of a network, which incorporates the topology of the network by considering the distance between nodes. Our approach generalizes the usual (co)variance to the setting of weighted networks and retains many of its intuitive and desired properties. To illustrate the application of these new measures in practice, we use them to analyze two empirical networks of mathematical concepts built with data from Wikipedia and a collection of scientific papers retrieved from ArXiv. Our approach allows for a unified and intuitive treatment of the structural data (relations between concepts) and functional data (usage of concepts in papers). Since the variance and covariance are general-purpose statistical tools, these new metrics may find application in multiple fields, like neuroscience, economics or social network analysis.
Preprint of the paper in arXiv: https://arxiv.org/abs/2008.09155