Beate Franke | Searcharxiv

arXiv2016

Network modularity in the presence of covariates

We characterize the large-sample properties of network modularity in the presence of covariates, under a natural and flexible nonparametric null model. This provides for the first time an objective measure of whether or not a particular value of modularity is meaningful. In particular, our results quantify the strength of the relation between observed community structure and the interactions in a network. Our technical contribution is to provide limit theorems for modularity when a community assignment is given by nodal features or covariates. These theorems hold for a broad class of network models over a range of sparsity regimes, as well as weighted, multi-edge, and power-law networks. This allows us to assign $p$-values to observed community structure, which we validate using several benchmark examples in the literature. We conclude by applying this methodology to investigate a multi-edge network of corporate email interactions.

math.ST↗

arXiv2015

Statistical Inference, Learning and Models in Big Data

The need for new methods to deal with big data is a common theme in most scientific fields, although its definition tends to vary with the context. Statistical ideas are an essential part of this, and as a partial response, a thematic program on statistical inference, learning, and models in big data was held in 2015 in Canada, under the general direction of the Canadian Statistical Sciences Institute, with major funding from, and most activities located at, the Fields Institute for Research in Mathematical Sciences. This paper gives an overview of the topics covered, describing challenges and strategies that seem common to many different areas of application, and including some examples of applications to make these challenges and strategies more concrete.

stat.ML↗