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Temporal networks consisting of timestamped interactions between a set of nodes provide a useful representation for analyzing complex networked systems that evolve over time. Beyond pairwise interactions between nodes, temporal motifs capture patterns of higher-order interactions such as directed triangles over short time periods. We propose temporal motif participation profiles (TMPPs) to capture the behavior of nodes in temporal motifs. Two nodes with similar TMPPs take similar positions within temporal motifs, possibly with different nodes. TMPPs serve as unsupervised embeddings for nodes in temporal networks that are directly interpretable, as each entry denotes the frequency at which a node participates in a particular position in a specific temporal motif. We demonstrate that clustering TMPPs reveals groups of nodes with similar roles in a temporal network through simulation experiments and a case study on a network of militarized interstate disputes. 

Some of the simplest, yet most frequently used predictors in statistics and machine learning use weighted linear combinations of features. Such linear predictors can model non-linear relationships between features by adding interaction terms corresponding to the products of all pairs of features. We consider the problem of accurately estimating coefficients for interaction terms in linear predictors. We hypothesize that the coefficients for different interaction terms have an approximate low-dimensional structure and represent each feature by a latent vector in a low-dimensional space. This low-dimensional representation can be viewed as a structured regularization approach that further mitigates overfitting in high-dimensional settings beyond standard regularizers such as the lasso and elastic net. We demonstrate that our approach, called LIT-LVM, achieves superior prediction accuracy compared to the elastic net, hierarchical lasso, and factorization machines on a wide variety of simulated and real data, particularly when the number of interaction terms is high compared to the number of samples. LIT-LVM also provides low-dimensional latent representations for features that are useful for visualizing and analyzing their relationships. 

Abstract Dynamic or temporal networks enable representation of time-varying edges between nodes. Conventional adjacency-based data structures used for storing networks such as adjacency lists were designed without incorporating time and can thus quickly retrieve all edges between two sets of nodes (a node-based slice ) but cannot quickly retrieve all edges that occur within a given time interval (a time-based slice ). We propose a hybrid data structure for storing temporal networks that stores edges in both an adjacency dictionary, enabling rapid node-based slices, and an interval tree, enabling rapid time-based slices. Our hybrid structure also enables compound slices , where one needs to slice both over nodes and time, either by slicing first over nodes or slicing first over time. We further propose an approach for predictive compound slicing, which attempts to predict whether a node-based or time-based compound slice is more efficient. We evaluate our hybrid data structure on many real temporal network data sets and find that they achieve much faster slice times than existing data structures with only a modest increase in creation time and memory usage. 

Networks and temporal point processes serve as fundamental building blocks for modeling complex dynamic relational data in various domains. We propose the latent space Hawkes (LSH) model, a novel generative model for continuous-time networks of relational events, using a latent space representation for nodes. We model relational events between nodes using mutually exciting Hawkes processes with baseline intensities dependent upon the distances between the nodes in the latent space and sender and receiver specific effects. We demonstrate that our proposed LSH model can replicate many features observed in real temporal networks including reciprocity and transitivity, while also achieving superior prediction accuracy and providing more interpretable fits than existing models. 

The stochastic block model (SBM) is one of the most widely used generative models for network data. Many continuous-time dynamic network models are built upon the same assumption as the SBM: edges or events between all pairs of nodes are conditionally independent given the block or community memberships, which prevents them from reproducing higher-order motifs such as triangles that are commonly observed in real networks. We propose the multivariate community Hawkes (MULCH) model, an extremely flexible community-based model for continuous-time networks that introduces dependence between node pairs using structured multivariate Hawkes processes. We fit the model using a spectral clustering and likelihood-based local refinement procedure. We find that our proposed MULCH model is far more accurate than existing models both for predictive and generative tasks. 

With the prevalence of interaction on social media, data compiled from these networks are perfect for analyzing social trends. One such trend that this paper aims to address is political homophily. Evidence of political homophily is well researched and indicates that people have a strong tendency to interact with others with similar political ideologies. Additionally, as links naturally form in a social network, either through recommendations or indirect interaction, new links are very likely to reinforce communities. This serves to make social media more insulated and ultimately more polarizing. We aim to address this problem by providing link recommendations that will reduce network homophily. We propose several variants of common neighbor-based link prediction algorithms that aim to recommend links to users who are similar but also would decrease homophily. We demonstrate that acceptance of these recommendations can indeed reduce the homophily of the network, whereas acceptance of link recommendations from a standard common neighbors algorithm does not.