No abstract

Nodes residing in different parts of a graph can have similar structural roles within their local network topology. The identification of such roles provides key insight into the organization of networks and can be used for a variety of machine learning tasks. However, learning structural representations of nodes is a challenging problem, and it has typically involved manually specifying and tailoring topological features for each node. In this paper, we develop GraphWave, a method that represents each node's network neighborhood via a low-dimensional embedding by leveraging heat wavelet diffusion patterns. Instead of training on hand-selected features, GraphWave learns these embeddings in an unsupervised way. We mathematically prove that nodes with similar network neighborhoods will have similar GraphWave embeddings even though these nodes may reside in very different parts of the network. GraphWave runtime scales linearly with the number of edges and experiments in a variety of different settings demonstrate GraphWave's real-world potential for capturing structural roles in networks. All in all, GraphWave outperforms existing state-of-the-art baselines in every experiment, by as much as 137%.

SummaryData analysis workflows in many scientific domains have become increasingly complex and flexible. To assess the impact of this flexibility on functional magnetic resonance imaging (fMRI) results, the same dataset was independently analyzed by 70 teams, testing nine ex-ante hypotheses. The flexibility of analytic approaches is exemplified by the fact that no two teams chose identical workflows to analyze the data. This flexibility resulted in sizeable variation in hypothesis test results, even for teams whose statistical maps were highly correlated at intermediate stages of their analysis pipeline. Variation in reported results was related to several aspects of analysis methodology. Importantly, meta-analytic approaches that aggregated information across teams yielded significant consensus in activated regions across teams. Furthermore, prediction markets of researchers in the field revealed an overestimation of the likelihood of significant findings, even by researchers with direct knowledge of the dataset. Our findings show that analytic flexibility can have substantial effects on scientific conclusions, and demonstrate factors related to variability in fMRI. The results emphasize the importance of validating and sharing complex analysis workflows, and demonstrate the need for multiple analyses of the same data. Potential approaches to mitigate issues related to analytical variability are discussed.

From longitudinal biomedical studies to social networks, graphs have emerged as a powerful framework for describing evolving interactions between agents in complex systems. In such studies, after pre-processing, the data can be represented by a set of graphs, each graph represents a system's state at a different point in time or space. The analysis of the system's dynamics depends on the selection of the appropriate analytical tools. In particular, after specifying properties characterizing similarities between states, a critical step lies in the choice of a distance between graphs capable of reflecting such similarities.While the literature offers a number of distances that one could a priori choose from, their properties have been little investigated and no guidelines regarding the choice of such a distance have yet been provided. In particular, most graph distances consider that the nodes are exchangeable and do not take into account node identities. Accounting for the alignment of the graphs enables us to enhance these distances' sensitivity to perturbations in the network and detect important changes in graph dynamics. Thus the selection of an adequate metric is a decisive -yet delicate -practical matter.In the spirit of Goldenberg, Zheng and Fienberg's seminal 2009 review [21], the purpose of this article is to provide an overview of commonly-used graph distances and an explicit characterization of the structural changes that they are best able to capture. To see how this translates in real-life situations, we use as a guiding thread to our discussion the application of these distances to the analysis of both a longitudinal microbiome dataset and a brain fMRI study. We show examples of using permutation tests to detect the effect of covariates on the graphs' variability. Finally synthetic examples provide intuition as to the qualities and drawbacks of the different distances. Above all, we provide some guidance for choosing one distance over another in certain types of applications.Finally, extending the scope of our analysis from temporal to spatial dynamics, we show an application of these different distances to a network created from worldwide recipes.

The correct evaluation of the reproductive number R for COVID-19 is central in the quantification of the potential scope of the pandemic and the selection of an appropriate course of action. In most models, R is modeled as a constant -effectively averaging out the inherent variability of the transmission process due to varying individual contact rates, population densities, or temporal factors amongst many. Yet, due to the exponential nature of epidemic growth, the error due to this simplification can be rapidly amplified, and its extent remains unknown. How can this intrinsic variability be percolated into epidemic models, and its impact, better quantified? We study this question here through a Bayesian perspective that captures at scale the heterogeneity of a population and environmental conditions, creating a bridge between the traditional agent-based and compartmental approaches. We use our model to simulate the spread as well as the impact of different social distancing strategies on real COVID-19 data, and highlight the significant impact of the heterogeneity. We emphasize that the contribution of this paper focuses on discussing the importance of the impact of R's heterogeneity on uncertainty quantification from a statistical viewpoint, rather than developing new predictive models.