An official website of the United States government
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.
more »
« less
This content will become publicly available on February 10, 2026
A Latent Space Approach to Inferring Distance-Dependent Reciprocity in Directed Networks
Reciprocity, or the stochastic tendency for actors to form mutual relationships, is an essential characteristic of directed network data. Existing latent space approaches to modelling directed networks are severely limited by the assumption that reciprocity is homogeneous across the network. In this work, we introduce a new latent space model for directed networks that can model heterogeneous reciprocity patterns that arise from the actors' latent distances. Furthermore, existing conditionally edge‐independent latent space models are nested within the proposed model class, which allows for meaningful model comparisons. We introduce a Bayesian inference procedure to infer the model parameters using Hamiltonian Monte Carlo. Lastly, we use the proposed method to infer different reciprocity patterns in an advice network among lawyers, an information‐sharing network between employees at a manufacturing company and a friendship network between high school students.
more »
« less
- Award ID(s):
- 2345043
- PAR ID:
- 10589899
- Publisher / Repository:
- Wiley
- Date Published:
- Journal Name:
- Stat
- Volume:
- 14
- Issue:
- 1
- ISSN:
- 2049-1573
- Page Range / eLocation ID:
- e70042
- Subject(s) / Keyword(s):
- Bayesian inference Hamiltonian Monte Carlo latent space network model reciprocity social networks
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
Abstract Reciprocity in social networks is a measure of information exchange between two individuals, and indicates interaction patterns between pairs of users. A recent study finds that the reciprocity coefficient of a classical directed preferential attachment (PA) model does not match empirical evidence. Towards remedying this deficiency, we extend the classical three-scenario directed PA model by adding a parameter that controls the probability of creating a reciprocal edge. This proposed model also allows edge creation between two existing nodes, making it a realistic candidate for fitting to datasets. We provide and compare two estimation procedures for fitting the new reciprocity model and demonstrate the methods on simulated and real datasets. One estimation method requires careful analysis of the heavy tail properties of the model. The fitted models provide a good match with the empirical tail distributions of both in- and out-degrees but other mismatched diagnostics suggest that further generalization of the model is warranted.more » « less
-
Graph structured data are abundant in the real world. Among different graph types, directed acyclic graphs (DAGs) are of particular interest to machine learning researchers, as many machine learning models are realized as computations on DAGs, including neural networks and Bayesian networks. In this paper, we study deep generative models for DAGs, and propose a novel DAG variational autoencoder (D-VAE). To encode DAGs into the latent space, we leverage graph neural networks. We propose an asynchronous message passing scheme that allows encoding the computations on DAGs, rather than using existing simultaneous message passing schemes to encode local graph structures. We demonstrate the effectiveness of our proposed DVAE through two tasks: neural architecture search and Bayesian network structure learning. Experiments show that our model not only generates novel and valid DAGs, but also produces a smooth latent space that facilitates searching for DAGs with better performance through Bayesian optimization.more » « less
-
Undirected, binary network data consist of indicators of symmetric relations between pairs of actors. Regression models of such data allow for the estimation of effects of exogenous covariates on the network and for prediction of unobserved data. Ideally, estimators of the regression parameters should account for the inherent dependencies among relations in the network that involve the same actor. To account for such dependencies, researchers have developed a host of latent variable network models; however, estimation of many latent variable network models is computationally onerous and which model is best to base inference upon may not be clear. We propose the probit exchangeable (PX) model for undirected binary network data that is based on an assumption of exchangeability, which is common to many of the latent variable network models in the literature. The PX model can represent the first two moments of any exchangeable network model. We leverage the EM algorithm to obtain an approximate maximum likelihood estimator of the PX model that is extremely computationally efficient. Using simulation studies, we demonstrate the improvement in estimation of regression coefficients of the proposed model over existing latent variable network models. In an analysis of purchases of politically aligned books, we demonstrate political polarization in purchase behavior and show that the proposed estimator significantly reduces runtime relative to estimators of latent variable network models, while maintaining predictive performance.more » « less
-
Summary Latent space models are frequently used for modelling single-layer networks and include many popular special cases, such as the stochastic block model and the random dot product graph. However, they are not well developed for more complex network structures, which are becoming increasingly common in practice. In this article we propose a new latent space model for multiplex networks, i.e., multiple heterogeneous networks observed on a shared node set. Multiplex networks can represent a network sample with shared node labels, a network evolving over time, or a network with multiple types of edges. The key feature of the proposed model is that it learns from data how much of the network structure is shared between layers and pools information across layers as appropriate. We establish identifiability, develop a fitting procedure using convex optimization in combination with a nuclear-norm penalty, and prove a guarantee of recovery for the latent positions provided there is sufficient separation between the shared and the individual latent subspaces. We compare the model with competing methods in the literature on simulated networks and on a multiplex network describing the worldwide trade of agricultural products.more » « less
