Understanding the Behavior of Large Networks
Abstract
In this talk – which will be accessible to a general audience – we show how the asymptotic behavior of random networks gives rise to universal statistical summaries. These summaries are related to concepts that are well understood in the other contexts outside of Big Data – such as stationarity and ergodicity – but whose extension to networks requires recent developments from the theory of graph limits and the corresponding analog of de Finetti’s theorem. We introduce a new tool based on these summaries, which we call a network histogram, obtained by fitting a statistical model called a blockmodel to a large network. Blocks of edges play the role of histogram bins, and so-called network community sizes that of histogram bandwidths or bin sizes. For more details, see recent work in the Proceedings of the National Academy of Sciences (doi:10.1073/pnas.1400374111, with Sofia Olhede) and the Annals of Statistics (doi:10.1214/13-AOS1173, with David Choi).
Background
Patrick J. Wolfe is Professor of Statistics and Honorary Professor of Computer Science at University College London, where he is Executive Director of the UCL Big Data Institute and a Royal Society and UK EPSRC Mathematical Sciences Established Career Research Fellow. He received the PhD degree from Cambridge and from 2001-2004 held a Fellowship and College Lectureship in Engineering and Computer Science there. Prior to joining UCL he was then Assistant (2004-2008) and Associate (2008-2011) Professor at Harvard University, where he received the Presidential Early Career Award from the White House in 2009 for contributions to signal and image processing. Externally to UCL, Prof. Wolfe currently serves on the Research Section Committee of the Royal Statistical Society, on the Program Committee of the 2015 Joint Statistical Meetings, and as an organizer of the 2016 Newton Institute 6-month programme on Theoretical Foundations for Statistical Network Analysis.
Personal web page.
Research Interests
The mathematics of Big Data. Modelling and inference for graphs and networks; statistical imaging and image processing; time series and time-frequency analysis; audio signal processing and acoustic modelling.