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Register a new userStructural Patterns and Generative Models of Real-world Hypergraphs
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Graphs have been utilized as a powerful tool to model pairwise relationships between people or objects. Such structure is a special type of a broader concept referred to as hypergraph, in which each hyperedge may consist of an arbitrary number of nodes, rather than just two. A large number of real-world datasets are of this form - for example, list of recipients of emails sent from an organization, users participating in a discussion thread or subject labels tagged in an online question. However, due to complex representations and lack of adequate tools, little attention has been paid to exploring the underlying patterns in these interactions. In this work, we empirically study a number of real-world hypergraph datasets across various domains. In order to enable thorough investigations, we introduce the multi-level decomposition method, which represents each hypergraph by a set of pairwise graphs. Each pairwise graph, which we refer to as a k-level decomposed graph, captures the interactions between pairs of subsets of k nodes. We empirically find that at each decomposition level, the investigated hypergraphs obey five structural properties. These properties serve as criteria for evaluating how realistic a hypergraph is, and establish a foundation for the hypergraph generation problem. We also propose a hypergraph generator that is remarkably simple but capable of fulfilling these evaluation metrics, which are hardly achieved by other baseline generator models.
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Complex network theory aims to model and analyze complex systems that consist of multiple and interdependent components. Among all studies on complex networks, topological structure analysis is of the most fundamental importance, as it represents a natural route to understand the dynamics, as well as to synthesize or optimize the functions, of networks. A broad spectrum of network structural patterns have been respectively reported in the past decade, such as communities, multipartites, hubs, authorities, outliers, bow ties, and others. Here, we show that most individual real-world networks demonstrate multiplex structures. That is, a multitude of known or even unknown (hidden) patterns can simultaneously situate in the same network, and moreover they may be overlapped and nested with each other to collaboratively form a heterogeneous, nested or hierarchical organization, in which different connective phenomena can be observed at different granular levels. In addition, we show that the multiplex structures hidden in exploratory networks can be well defined as well as effectively recognized within an unified framework consisting of a set of proposed concepts, models, and algorithms. Our findings provide a strong evidence that most real-world complex systems are driven by a combination of heterogeneous mechanisms that may collaboratively shape their ubiquitous multiplex structures as we observe currently. This work also contributes a mathematical tool for analyzing different sources of networks from a new perspective of unveiling multiplex structures, which will be beneficial to multiple disciplines including sociology, economics and computer science.
Objective: The COVID-19 pandemic has created many challenges that need immediate attention. Various epidemiological and deep learning models have been developed to predict the COVID-19 outbreak, but all have limitations that affect the accuracy and robustness of the predictions. Our method aims at addressing these limitations and making earlier and more accurate pandemic outbreak predictions by (1) using patients EHR data from different counties and states that encode local disease status and medical resource utilization condition; (2) considering demographic similarity and geographical proximity between locations; and (3) integrating pandemic transmission dynamics into deep learning models. Materials and Methods: We proposed a spatio-temporal attention network (STAN) for pandemic prediction. It uses an attention-based graph convolutional network to capture geographical and temporal trends and predict the number of cases for a fixed number of days into the future. We also designed a physical law-based loss term for enhancing long-term prediction. STAN was tested using both massive real-world patient data and open source COVID-19 statistics provided by Johns Hopkins university across all U.S. counties. Results: STAN outperforms epidemiological modeling methods such as SIR and SEIR and deep learning models on both long-term and short-term predictions, achieving up to 87% lower mean squared error compared to the best baseline prediction model. Conclusions: By using information from real-world patient data and geographical data, STAN can better capture the disease status and medical resource utilization information and thus provides more accurate pandemic modeling. With pandemic transmission law based regularization, STAN also achieves good long-term prediction performance.
Recent advances in differentiable rendering have sparked an interest in learning generative models of textured 3D meshes from image collections. These models natively disentangle pose and appearance, enable downstream applications in computer graphics, and improve the ability of generative models to understand the concept of image formation. Although there has been prior work on learning such models from collections of 2D images, these approaches require a delicate pose estimation step that exploits annotated keypoints, thereby restricting their applicability to a few specific datasets. In this work, we propose a GAN framework for generating textured triangle meshes without relying on such annotations. We show that the performance of our approach is on par with prior work that relies on ground-truth keypoints, and more importantly, we demonstrate the generality of our method by setting new baselines on a larger set of categories from ImageNet - for which keypoints are not available - without any class-specific hyperparameter tuning. We release our code at https://github.com/dariopavllo/textured-3d-gan
Much research has been done on studying the diffusion of ideas or technologies on social networks including the textit{Influence Maximization} problem and many of its variations. Here, we investigate a type of inverse problem. Given a snapshot of the diffusion process, we seek to understand if the snapshot is feasible for a given dynamic, i.e., whether there is a limited number of nodes whose initial adoption can result in the snapshot in finite time. While similar questions have been considered for epidemic dynamics, here, we consider this problem for variations of the deterministic Linear Threshold Model, which is more appropriate for modeling strategic agents. Specifically, we consider both sequential and simultaneous dynamics when deactivations are allowed and when they are not. Even though we show hardness results for all variations we consider, we show that the case of sequential dynamics with deactivations allowed is significantly harder than all others. In contrast, sequential dynamics make the problem trivial on cliques even though its complexity for simultaneous dynamics is unknown. We complement our hardness results with structural insights that can help better understand diffusions of social networks under various dynamics.
Mobile health applications, including those that track activities such as exercise, sleep, and diet, are becoming widely used. Accurately predicting human actions is essential for targeted recommendations that could improve our health and for personalization of these applications. However, making such predictions is extremely difficult due to the complexities of human behavior, which consists of a large number of potential actions that vary over time, depend on each other, and are periodic. Previous work has not jointly modeled these dynamics and has largely focused on item consumption patterns instead of broader types of behaviors such as eating, commuting or exercising. In this work, we develop a novel statistical model for Time-varying, Interdependent, and Periodic Action Sequences. Our approach is based on personalized, multivariate temporal point processes that model time-varying action propensities through a mixture of Gaussian intensities. Our model captures short-term and long-term periodic interdependencies between actions through Hawkes process-based self-excitations. We evaluate our approach on two activity logging datasets comprising 12 million actions taken by 20 thousand users over 17 months. We demonstrate that our approach allows us to make successful predictions of future user actions and their timing. Specifically, our model improves predictions of actions, and their timing, over existing methods across multiple datasets by up to 156%, and up to 37%, respectively. Performance improvements are particularly large for relatively rare and periodic actions such as walking and biking, improving over baselines by up to 256%. This demonstrates that explicit modeling of dependencies and periodicities in real-world behavior enables successful predictions of future actions, with implications for modeling human behavior, app personalization, and targeting of health interventions.
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