Cascade model with Dirichlet process for analyzing multiple dyadic matrices

Abstract

Dyadic matrices are natural data representations in a wide range of domains. A dyadic matrix often involves two types of abstract objects and is based on observations of pairs of elements with one element from each object. Owing to the increasing needs from practical applications, dyadic data analysis has recently attracted increasing attention and many techniques have been developed. However, most existing approaches, such as co-clustering and relational reasoning, only handle a single dyadic table and lack flexibility to perform prediction using multiple dyadic matrices. In this article, we propose a general nonparametric Bayesian framework with a cascaded structure to model multiple dyadic matrices and then describe an efficient hybrid Gibbs sampling algorithm for posterior inference and analysis. Empirical evaluations using both synthetic data and real data show that the proposed model captures the hidden structure of data and generalizes the predictive inference in a unique way.

Keywords:

• cascade model
• Dirichlet process
• ANOVA model
• interaction
• hybrid Gibbs sampler

Acknowledgement

We thank Dr Jonathan Hosking for reviewing and kindly providing with revision suggestions.

Notes

For the sake of simplicity, we use the example with three abstract objects and two matrices to demonstrate our method. However, the proposed framework can be naturally adapted to more complicated cases with more than three objects and two dyadic matrices.

In the example of predicting authors for a given article, one can convert the continuous prediction results [stilde] _ij to obtain binary authorship via any reasonable link functions or thresholding.

The original FPCA method solves the completion problem for a continuous-valued matrix. Here, we use a simple heuristic to convert to binary values by thresholding with the consideration of the prior.