Week 12.12.2021 – 18.12.2021

We investigate the statistics of articulation points and bredges (bridge-edges) in complex networks in which bonds are randomly removed in a percolation process. Because of the heterogeneous structure of a complex network, the probability of a node to be an articulation point, or the probability of an edge to be a bredge will not be homogeneous across the network. We therefore analyze full distributions of articulation point probabilities as well as bredge probabilities, using a message-passing or cavity approach to the problem. Our methods allow us to obtain these distributions, both for large single instances of networks and for ensembles of networks in the configuration model class in the thermodynamic limit, through a single unified approach. We also evaluate deconvolutions of these distributions according to degrees of the node or the degrees of both adjacent nodes in the case of bredges. We obtain closed form expressions for the large mean degree limit of Erdos-Renyi networks. Moreover, we reveal, and are able to rationalize, a significant amount of structure in the evolution of articulation point and bredge probabilities in response to random bond removal. We find that full distributions of articulation point and bredge probabilities in real networks and in their randomized counterparts may exhibit significant differences even where average articulation point and bredge probabilities don't. We argue that our results could be exploited in a variety of applications, including approaches to network dismantling or to vaccination and islanding strategies to prevent the spread of epidemics or of blackouts in process networks.

Nicholas Iles is a Senior Director of Data Science Engineering at Choreograph, who specialise in agent-based modelling. He graduated from King's with a PhD in Applied Maths in 2016. This careers talk is part of the series ‘on the transition from academia to industry’ by former PhD students organised by Professor Tiziana Di Matteo.

Meeting link below

https://teams.microsoft.com/l/meetup-join/19%3ameeting_ODdjYWFmMmEtM2VjNS00ZTE2LThlOTEtMDAxM2ZhYTVkY2Vh%40thread.v2/0?context=%7b%22Tid%22%3a%228370cf14-16f3-4c16-b83c-724071654356%22%2c%22Oid%22%3a%22d0ab862e-769f-41f8-ac51-282fb61fd3c4%22%7d

Leave-one-out cross-validation (LOO-CV) is a popular method for estimating out-of-sample predictive accuracy. However, computing LOO-CV criteria can be computationally expensive due to the need to fit the model multiple times. In the Bayesian context, importance sampling provides a possible solution but classical approaches can easily produce estimators whose variance is infinite, making them potentially unreliable. Here we propose and analyze a novel mixture estimator to compute Bayesian LOO-CV criteria. Our method retains the simplicity and computational convenience of classical approaches, while guaranteeing finite variance of the resulting estimators. Both theoretical and numerical results are provided to illustrate the improved robustness and efficiency. The computational benefits are particularly significant in high-dimensional problems, allowing to perform Bayesian LOO-CV for a broader range of models.