arXiv subjects

P-A. G. Maugis

Publications and source records attributed to P-A. G. Maugis.

3 recordsLinked to original sources

arXiv2019

Statistical inference for network samples using subgraph counts

We consider that a network is an observation, and a collection of observed networks forms a sample. In this setting, we provide methods to test whether all observations in a network sample are drawn from a specified model. We achieve this by deriving, under the null of the graphon model, the joint asymptotic properties of average subgraph counts as the number of observed networks increases but the number of nodes in each network remains finite. In doing so, we do not require that each observed network contains the same number of nodes, or is drawn from the same distribution. Our results yield joint confidence regions for subgraph counts, and therefore methods for testing whether the observations in a network sample are drawn from: a specified distribution, a specified model, or from the same model as another network sample. We present simulation experiments and an illustrative example on a sample of brain networks where we find that highly creative individuals' brains present significantly more short cycles.

stat.ME↗

arXiv2017

Fast counting of medium-sized rooted subgraphs

We prove that counting copies of any graph $F$ in another graph $G$ can be achieved using basic matrix operations on the adjacency matrix of $G$. Moreover, the resulting algorithm is competitive for medium-sized $F$: our algorithm recovers the best known complexity for rooted 6-clique counting and improves on the best known for 9-cycle counting. Underpinning our proofs is the new result that, for a general class of graph operators, matrix operations are homomorphisms for operations on rooted graphs.

cs.DM↗

arXiv2016

Event Conditional Correlation: Or How Non-Linear Linear Dependence Can Be

Entries of datasets are often collected only if an event occurred: taking a survey, enrolling in an experiment and so forth. However, such partial samples bias classical correlation estimators. Here we show how to correct for such sampling effects through two complementary estimators of event conditional correlation: the correlation of two random variables conditional on a given event. First, we provide under minimal assumptions proof of consistency and asymptotic normality for the proposed estimators. Then, through synthetic examples, we show that these estimators behave well in small-sample and yield powerful methodologies for non-linear regression as well as dependence testing. Finally, by using the two estimators in tandem, we explore counterfactual dependence regimes in a financial dataset. By so doing we show that the contagion which took place during the 2007--2011 financial crisis cannot be explained solely by increased financial risk.

stat.ME↗