On Graph Limits as Models for Interaction Data

Abstract

Network data has become a staple in many different applications, ranging from ecology, to neuroscience and systems biology. Its inference will of course depend on the application where we collect the network data, but I will discuss some general principles based on probabilistic symmetries such as permutation invariance. Just like other probabilistic invariances, the distributional invariance to permuting indices of a matrix of interactions implies a representation theorem (the Aldous-Hoover theorem). This representation is in terms of a graph limit function, or graphon. I will discuss the representation, how to make inferences based on this representation, what to do if distributional permutation invariance does not hold, and what to do if we have additional information such as time stamp of interactions, multiple interactions or additional covariate data.

Our Speaker

Sofia Olhede is a professor of Statistics at EPFL in Lausanne Switzerland and an honorary professor of statistics at UCL, as well as an honorary senior research associate of mathematics. She received the M.Sc. and Ph.D. degrees in mathematics from Imperial College London, London, U.K., in 2000 and 2003, respectively. She was a Lecturer (2002–2006) and a Senior Lecturer (2006–2007) with the Mathematics Department, Imperial College London. In 2007, she joined the Department of Statistical Science, University College London, London, U.K., as a Professor. In 2019, she moved to the Institute of Mathematics, École Polytechnique Fédérale de Lausanne, where she holds the Chair of statistical data science. Dr. Olhede is a fellow of the Royal Statistical Society and the Institute of Mathematical Statistics.

She has held multiple research fellowships including a UK EPSRC leadership fellowship and an ERC consolidator award. Her research interests are modelling and analysing dependent data such as time series, random fields, point patterns and network data.