### Program

When? Thursday, September 17 2020, 13:00 - 18:00 CET

Where? Rome, Italy (Online Event)

We are proud to present a high-quality program with speakers from different communities. Speakers who want to publish their talks after the satellite can send their slides via E-Mail.

Time Presenter
13:00 - 13:15 Organizers
Opening Statement
Session chair: Giona Casiraghi
13:15 - 14:00 Panel Discussion: Comparing Simplicial Complexes, Hypergraphs, and Temporal Networks as representations of higher order interactions.
Yamir Moreno, Ingo Scholtes, Giovanni Petri, Ann Sizemore Blevins, Leo Torres
14:00 - 14:15 Virtual Coffee Break
Session chair: Giona Casiraghi
14:15 - 14:45 Laetitia Gauvin (ISI Foundation, Torino, Italy)
Invited Talk: tbd Network Embedding and spreading process
14:45 - 15:15 Jean-Gabriel Young (Department of Computer Science, University of Vermont, USA)
Invited Talk: Hypergraph reconstruction from network data Networks are used as the most common mathematical abstraction to describe a wide variety of complex systems. In many situations, however, it is not enough to describe the pairwise interactions between units, as the fundamental interactions involves more than a pair of elements simultaneously. Unfortunately, the vast majority of available data lacks this kind of higher-order information, and are composed only of pairwise projections. Here we introduce a nonparametric Bayesian approach that reconstructs the higher-order interactions given only network data. Our method is based on the principle of parsimony, and does not needlessly reconstruct higher-order structures when there is no statistical evidence available. We demonstrate that our approach successfully uncovers higher-order interactions in synthetic and empirical network data.
15:15 - 15:30 Virtual Coffee Break
Session chair: Laurence Brandenberger
15:30 - 16:00 Luka Petrović (Department of Computer Science, University of Zürich, CH)
Invited Talk: Bayesian Selection of Optimal Higher-Order Network Models The analysis of relational data from the perspective of graphs or networks gives important insights into the structure of complex systems. However, rich data sources increasingly capture more than just the network topology, which introduces both new challenges and opportunities. One example are high-resolution time-stamped data, which enable us to infer how information propagates through a network, how humans travel in transportation networks, or in which chronological order social interactions occur. Such time series data naturally gives rise to \emph{paths}, i.e. ordered and non-dyadic sequences of nodes that capture the sequence in which the elements of a complex system influence each other. Due to the fundamentally non-dyadic nature of paths, the analysis of such data in terms of graph or network models is an open challenge. To address this challenge, researchers have proposed different types of higher-order network models. Those models are able to capture temporal-topological patterns in time series data on networks and give important new insights into the structure and dynamics of complex systems. A fundamental issue in those works is model selection, i.e. the need to determine the optimal order of a higher-order model given the patterns in the data. It is aggravated by the high dimensionality of higher-order models, which increases both the potential of overfitting as well as the amount of data required to reasonably fit a model. Previous works have mainly addressed this issue using heuristic approaches, information-theoretic methods, hypothesis testing techniques. Existing works on Bayesian selection of higher-order models in categorical sequence data did not account for the fact that the sequence of nodes on paths is constrained by an underlying network topology. Addressing this gap, we develop a Bayesian technique to select the optimal order of higher-order models based on data capturing paths in networks. Extending the previously proposed modelling framework, our method includes a prior for transition probabilities that accounts for constraints imposed on paths in a known underlying network. We evaluate our method in synthetically generated data with a varying number of paths generated in random Erdos-Renyi networks, where the optimal order of a higher-order model is known. In the figure below we demonstrate our method to a data set with a known order of two, and compare it to the hypothesis testing technique. The results show that our Bayesian approach (bottom) outperforms the likelihood-based method (top) for small sample sizes (x-axis). Interestingly, the likelihood-based model selection does not give a uniform distribution of p-values even if (i) the null hypothesis is correct (orange curve in top figure) and (ii) the sample size is large. Hence, for large samples sizes (between $10^4$ and $10^7$ paths), the $p$-value threshold can not be interpreted as the type I error rate of the hypothesis test. Moreover, we observe a regime ($\approx 10^4 - 10^5$ paths) where the method wrongly rejects the correct null hypothesis with high probability. In this regime the distribution of the likelihood-ratio test strongly deviates from a chi-square distribution, which undermines the assumptions of the hypothesis test. This leads to a tendency to overfit and can be avoided by our Bayesian method (bottom). This approach consistently selects the correct order with high probability for all sample sizes larger than $300$ paths. Our work highlights the benefits of Bayesian techniques to select optimal models for time series data on networks. The proposed method scales to large data sets and has been implemented in the Open Source network analysis package pathpy. We compare our method to existing model selection techniques for higher-order models of paths in networks. Highlighting a link between network-based models of temporal network data and machine learning, our analysis shows under which circumstances higher-order models over- or underfit patterns in time series data on networks, and how we can utilize Bayesian methods to avoid this issue.
16:00 - 16:30 Benjamin W. Campbell (Department of Political Science, Ohio State University, USA)
Invited Talk: Detecting Heterogeneity and Inferring Latent Roles in Longitudinal Military Alliance Data
Network analysis has typically examined the formation of whole networks while neglecting variation within or across networks. These approaches neglect the particular roles actors may adopt within networks. While cross-sectional approaches for inferring latent roles exist, there is a paucity of approaches for considering roles in longitudinal networks. This talk explores the conceptual dynamics of temporally observed roles while deriving and introducing a novel statistical tool, the ego-TERGM, capable of uncovering these latent dynamics. Estimated through an Expectation–Maximization algorithm, the ego-TERGM is quick and accurate in classifying roles within a broader temporal network. An application to data on interstate military alliances highlights the model's utility.
16:30 - 17:00 Fernando Antônio Nóbrega Santos (Department of Anatomy and Neurosciences, Vrije Universiteit Amsterdam, Netherlands)
Invited Talk: Statistical mechanics meets stochastic topology, high-order networks, and complex systems Abstract: Over the past decades, methods and concepts of differential topology were used in classical statistical mechanics to describe phase transitions. In parallel, methods of stochastic topology were used to generalize the so-called giant component transition to simplicial complexes. In this talk, we show that it is possible to put those ideas together, by using methods of Topological Data Analysis (TDA) to characterize topological phase transitions in high-order networks and complex systems. Under certain conditions, topological phase transitions in networks are characterized by i) the zeros of the Euler characteristic (or the singularities of the Euler entropy); ii) the emergence of multidimensional topological holes in a network; and iii) signal changes in the mean node curvature of a network. The geometric nature of the transitions can be interpreted, under specific hypotheses, as an extension of percolation to high-dimensional objects. We illustrate those ideas in functional brain networks, both in healthy and disease groups, in empirical protein interaction networks, as well as other theoretical network models. Due to the universal character of phase transitions and noise robustness of TDA, our findings open perspectives towards establishing reliable topological and geometrical fingerprints for networks. Finally, inspired by the long-term relation between topology and theoretical physics, we point at the possibility of finding high-order network analogs to this relation that have the potential to lead to basic principles in network science.
17:00 - 17:30 Alice C. Schwarze (Department of Biology, University of Washington, USA)
Invited Talk: Motifs for processes on networks
The study of motifs in networks can help researchers uncover links between structure and function of networks in biology, ecology, the social sciences, and many other fields. Empirical studies of networks have identified feedback loops, feedforward loops, and several other small structures as motifs'' that occur frequently in real-world networks and may contribute by various mechanisms to important functions these systems. For many of these motifs, their mechanisms are unknown. We propose to distinguish between structure motifs'' (i.e., graphlets) in networks and process motifs'' (which we define as structured sets of walks) on networks and consider process motifs as building blocks of processes on networks. Using as examples the covariances and correlations in a multivariate Ornstein--Uhlenbeck process on a network, we demonstrate that the distinction between structure motifs and process motifs makes it possible to gain new, quantitative insights into mechanisms that contribute to important functions of dynamical systems on networks.
New DEMO Session
17:30 - 18:00 Jürgen Hackl (Department of Informatics, University of Zürich, CH)
Demo: PathPy 3
18:00 Organizers
Closing Statement