32,787 research outputs found
Nonparametric Bayes dynamic modeling of relational data
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
Probabilistic Latent Tensor Factorization Model for Link Pattern Prediction in Multi-relational Networks
This paper aims at the problem of link pattern prediction in collections of
objects connected by multiple relation types, where each type may play a
distinct role. While common link analysis models are limited to single-type
link prediction, we attempt here to capture the correlations among different
relation types and reveal the impact of various relation types on performance
quality. For that, we define the overall relations between object pairs as a
\textit{link pattern} which consists in interaction pattern and connection
structure in the network, and then use tensor formalization to jointly model
and predict the link patterns, which we refer to as \textit{Link Pattern
Prediction} (LPP) problem. To address the issue, we propose a Probabilistic
Latent Tensor Factorization (PLTF) model by introducing another latent factor
for multiple relation types and furnish the Hierarchical Bayesian treatment of
the proposed probabilistic model to avoid overfitting for solving the LPP
problem. To learn the proposed model we develop an efficient Markov Chain Monte
Carlo sampling method. Extensive experiments are conducted on several real
world datasets and demonstrate significant improvements over several existing
state-of-the-art methods.Comment: 19pages, 5 figure
- …