A Bayesian Dynamic Latent Space Model for Weighted Networks

2026-03-25

AI Summary

This work proposes a Bayesian dynamic latent space model tailored for weighted temporal networks exhibiting complex characteristics such as integer-valued edge weights, zero-inflation, dynamically evolving node latent positions, and time-varying sparsity. The model captures the temporal dependencies of node latent features through vector autoregression and, for the first time in latent space network modeling, incorporates both contemporaneous and lagged dependencies across nodes and latent dimensions. To enhance inference efficiency, a non-recursive block-updating multi-step sampler is developed, integrating auxiliary mixture sampling, Laplace approximation, and partially collapsed Gibbs sampling to substantially improve Markov chain mixing and computational scalability. The framework flexibly accommodates both integer and continuous edge weights and can be readily extended to static or dynamic settings, enabling accurate and efficient inference for complex temporal networks.

Technology Category

• Reasoning under Uncertainty: Relational Probabilistic Models
• Planning, Routing, and Scheduling: Temporal Planning
• Machine Learning: Probabilistic Circuits and Graphical Models

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Models for Web evolution
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

A new dynamic latent space eigenmodel (LSM) is proposed for weighted temporal networks. The model accommodates integer-valued weights, excess of zeros, time-varying node positions (features), and time-varying network sparsity. The latent positions evolve according to a vector autoregressive process that accounts for lagged and contemporaneous dependence across nodes and features, a characteristic neglected in the LSM literature. A Bayesian approach is used to address two of the primary sources of inference intractability in dynamic LSMs: latent feature estimation and the choice of latent space dimension. We employ an efficient auxiliary-mixture sampler that performs data augmentation and supports conditionally conjugate prior distributions. A point-process representation of the network weights and the finite-dimensional distribution of the latent processes are used to derive a multi-move sampler in which each feature trajectory is drawn in a single block, without recursions. This sampling strategy is new to the network literature and can significantly reduce computational time while improving chain mixing. To avoid trans-dimensional samplers, a Laplace approximation of the partial marginal likelihood is used to design a partially collapsed Gibbs sampler. Overall, our procedure is general, as it can be easily adapted to static and dynamic settings, as well as to other discrete or continuous weight distributions.

Problem

• weighted networks
• dynamic latent space model
• temporal networks
• Bayesian inference
• network sparsity

Innovation

• Bayesian dynamic latent space model
• vector autoregressive process
• multi-move sampler
• auxiliary-mixture sampler
• partially collapsed Gibbs sampler