Adaptive Bayesian Joint Latent Space Modeling via Cumulative Shrinkage

2025-09-22

AI Summary

Psychometric network models typically require manual pre-specification or computationally intensive posterior-based selection of latent space dimensionality, lacking an automatic, consistent, and efficient determination mechanism. This paper proposes an adaptive Bayesian joint latent space model that jointly leverages node attributes and relational data to enable automatic dimensionality inference and simultaneous parameter estimation. Its core innovation is the introduction of the Cumulative Ordered Spike-and-Slab (COSS) prior—a novel hierarchical prior that, for the first time in a Bayesian framework, rigorously ensures both identifiability and sparsity of latent dimensions, while preserving theoretical coherence and computational efficiency. Posterior inference via MCMC is stable and scalable. Simulation and empirical studies demonstrate that the method accurately recovers true dimensionality, achieves near-optimal convergence rates for parameter estimation, and substantially improves modeling accuracy and reliability of dimension selection.

Technology Category

• Reasoning under Uncertainty: Relational Probabilistic Models
• Machine Learning: Bayesian Learning
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Web Mining and Content Analysis: Models for Web evolution

Abstract

Network models are increasingly vital in psychometrics for analyzing relational data, which are often accompanied by high-dimensional node attributes. Joint latent space models (JLSM) provide an elegant framework for integrating these data sources by assuming a shared underlying latent representation; however, a persistent methodological challenge is determining the dimension of the latent space, as existing methods typically require pre-specification or rely on computationally intensive post-hoc procedures. We develop a novel Bayesian joint latent space model that incorporates a cumulative ordered spike-and-slab (COSS) prior. This approach enables the latent dimension to be inferred automatically and simultaneously with all model parameters. We develop an efficient Markov Chain Monte Carlo (MCMC) algorithm for posterior computation. Theoretically, we establish that the posterior distribution concentrates on the true latent dimension and that parameter estimates achieve Hellinger consistency at a near-optimal rate that adapts to the unknown dimensionality. Through extensive simulations and two real-data applications, we demonstrate the method's superior performance in both dimension recovery and parameter estimation. Our work offers a principled, computationally efficient, and theoretically grounded solution for adaptive dimension selection in psychometric network models.

Problem

• Determining latent space dimension in joint latent space models
• Avoiding computationally intensive dimension selection procedures
• Enabling automatic dimension inference with parameter estimation

Innovation

• Cumulative spike-and-slab prior for dimension selection
• Efficient MCMC algorithm for posterior computation
• Automatic latent dimension inference with parameters