Nonparametric Bayes dynamic modeling of relational data
This work addresses the challenge of analyzing time-varying relational data, such as financial co-movements, with a novel method that is incremental in its approach to dynamic modeling.
The authors tackled the problem of modeling dynamically evolving binary relational matrices by proposing a nonparametric Bayesian dynamic model that reduces dimensionality through a latent space representation, achieving computational tractability and automatically inferring the latent dimension via an efficient Gibbs sampler, with performance illustrated through simulations and an application to world financial markets.
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 Pòlya-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.