# Nonparametric Bayes dynamic modeling of relational data

arXiv: https://arxiv.org/abs/1311.4669 · HTML: https://mlsanity.com/paper/1311.4669/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Nov 2013.

## Built on by (most cited first, 8 of 8)

- [Spectral embedding for dynamic networks with stability guarantees](https://mlsanity.com/paper/2106.01282/) (2021)
- [Continuous Latent Position Models for Instantaneous Interactions](https://mlsanity.com/paper/2103.17146/) (2021)
- [A Latent Space Model for Multilayer Network Data](https://mlsanity.com/paper/2102.09560/) (2021)
- [Concentration inequalities for correlated network-valued processes with applications to community estimation and changepoint analysis](https://mlsanity.com/paper/2208.01365/) (2022)
- [A Probit Tensor Factorization Model For Relational Learning](https://mlsanity.com/paper/2111.03943/) (2021)
- [Factorized Fusion Shrinkage for Dynamic Relational Data](https://mlsanity.com/paper/2210.00091/) (2022)
- [Tensor State Space-based Dynamic Multilayer Network Modeling](https://mlsanity.com/paper/2506.02413/) (2025)
- [Dynamic Latent Space Modeling of Inhomogeneous Poisson Network Processes with Applications to International Relations](https://mlsanity.com/paper/2609.08813/) (2026)

## Abstract (arXiv)

Symmetric binary matrices representing relations among entities are commonly collected in many areas. Our focus is on dynamically evolving binary relational matrices, with interest being in inference on the relationship structure and prediction. We propose a nonparametric Bayesian dynamic model, which reduces dimensionality in characterizing the binary matrix through a lower-dimensional latent space representation, with the latent coordinates evolving in continuous time via Gaussian processes. By using a logistic mapping function from the probability matrix space to the latent relational space, we obtain a flexible and computational tractable formulation. Employing P`olya-Gamma data augmentation, an efficient Gibbs sampler is developed for posterior computation, with the dimension of the latent space automatically inferred. We provide some theoretical results on flexibility of the model, and illustrate performance via simulation experiments. We also consider an application to co-movements in world financial markets.