[Paper Review] A Bayesian Dynamic Latent Space Model for Weighted Networks

Roberto Casarin, Matteo Iacopini+1 more|arXiv (Cornell University)|Mar 25, 2026

Mental Health Research Topics0 citations

TL;DR

Introduces a Bayesian dynamic latent space eigenmodel for count-valued weighted networks with zero inflation, enabling time-varying node features and sparsity; employs auxiliary mixture data augmentation and a partially collapsed Gibbs sampler to infer latent space dimension and trajectories efficiently.

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.

Motivation & Objective

• Motivate and address the analysis of dynamic, weighted networks with counts and excess zeros.
• Propose a dynamic zero-inflated latent space eigenmodel where edge weights depend on latent feature similarity.
• Develop a scalable Bayesian inference scheme that jointly infers latent features, their dimension, and dynamic structure.
• Introduce computational innovations (auxiliary mixture sampler, AWOL sampling, Laplace-based dimension handling) to improve mixing and speed.
• Provide flexible model specifications (node-wise vs. feature-wise) to capture dependence and sparsity in temporal networks.

Proposed method

• Define y_{ij,t} as a zero-inflated Poisson with intensity bb_{ij,t} determined by latent features via log(bb_{ij,t}) = b5_i + b5_j + x_{i:,t}' Xi x_{j:,t}.
• Model latent features X_t with a matrix autoregression X_t = eb1 X_{t-1} ' + H_t, with H_t following a matrix normal distribution.
• Introduce an auxiliary allocation w_{ij,t} for zero inflation and a probit latent variable z_{ij,t} to handle zero-prone edges.
• Employ an improved auxiliary mixture sampler (IAMS) to convert Poisson likelihoods into conditionally Gaussian form for conjugate updates.
• Use a partially collapsed Gibbs sampler to infer the latent space dimension d and the latent trajectories without trans-dimensional moves.
• Provide two parsimonious parameterisations (node-wise vs. feature-wise) for the latent dynamics and discuss their implications.

Experimental results

Research questions

• RQ1 How can dynamic latent space models be extended to weighted, count-valued networks with excess zeros?
• RQ2 Can we infer both latent node features and the latent space dimension in a Bayesian framework for dynamic networks?
• RQ3 Does a feature-wise specification capturing contemporaneous node dependence improve inference over traditional node-wise approaches?
• RQ4 How can auxiliary data augmentation and partially collapsed sampling improve computation and mixing in dynamic LSMs for counts?
• RQ5 What are the practical implications of zero-inflated Poisson dynamics in real-world temporal networks (e.g., voting, trade, brain connectivity)?

Key findings

• The proposed dynamic zero-inflated latent space eigenmodel accommodates integer weights, excess zeros, time-varying node positions, and varying sparsity.
• An auxiliary-mixture sampler renders the Poisson part conditionally Gaussian, enabling conjugate updates and efficient MCMC.
• A novel AWOL-based sampler samples whole latent trajectories without loops, improving mixing and reducing computation.
• A Laplace-approximation-based partially collapsed Gibbs sampler avoids trans-dimensional moves for inferring latent dimension d.
• Two parameterisations (node-wise and feature-wise) with different priors (inverse-Wishart vs. graphical horseshoe) provide flexible handling of dependencies and high-dimensionality.
• The sampler jointly infers the latent space dimension alongside latent features, quantifying uncertainty rather than relying on fixed d or information criteria.