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Title: Distances on and between complex networks

Abstract:

Distance plays a pivotal role in statistics. Meanwhile, recent technologies and social networks have yielded large complex network data sets, which require customized statistical tools. From a mathematical viewpoint, these complex networks are graphs with non-trivial structures (in contrast to Erd枚s-R茅nyi graphs, for example). These networks are models of systemic phenomena and cases where individual-level analyses are insufficient. Such models are not only used in the study of social networks, but are also widely employed in neurology, biology, telecommunication and finance, among many areas of application. Unfortunately, however, distances on graphs are not clearly defined.

I will begin with a general introduction to complex networks, through a few illustrative examples. I will then introduce two key (statistical) problems in the analysis of complex networks, vertex clustering/community detection and the study of temporal graphs. Both these problems rely on distances.

Following this introduction, I will present our work on distances for use in the statistical analyses (unsupervised learning) of these novel complex data sets. I will focus on the tailoring of traditional, so-called 鈥済eneral purpose鈥� statistical techniques to the specific case of network data, through the use of these distances. I will also very briefly highlight possible applications for quantum and 鈥渜uantum-like鈥� computing.

This presentation is aimed at a broad mathematical sciences audience. No prior knowledge of graph theory or complex networks will be assumed.

Speaker

Pierre is a MITACS post-doctoral fellow at the University of Toronto, where he is affiliated with the Data Sciences Institute, the Mechanical & Industrial Engineering and Chemical Engineering Departments. His work is co-supervised by Prof. Yuri Lawryshyn of UofT and Prof. Cristian Bravo of the Statistics & Actuarial Sciences Department at the University of Western Ontario.

Pierre鈥檚 current research, which is partially supported by RBC, focuses on tailoring traditional statistical techniques to complex networks, with a view on fintech applications. In the past, he has extended traditional significance tests to network science problems such as clustering quality and clusterability. Prior to his current job, Pierre worked as a quantitative analyst in the financial industry and in a large research hospital and as a post-doctoral researcher in a high performance computing lab.

Meeting ID: 834 7786 5796

Passcode: None

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