Section: New Results

Approche bayésienne non paramétrique pour la factorisation de matrice binaire à faible rang avec loi de puissance

The following result has been obtained by Adrien Todeschini (CQFD member) and François Caron.

We introduce a low-rank Bayesian nonparametric (BNP) model for bipartite graphs. Recently, Caron (2012) proposed a BNP model where each node is given its own sociability parameter allowing to capture the power-law behavior of real world bipartite graphs. This model can be considered as a rank one nonnegative factorization of the adjacency matrix. Building on the compound random measures recently introduced by Griffin and Leisen (2014), we derive a rank p generalization of this model where each node is associated with a p-dimensional vector of sociability parameters accounting for several latent dimensions. While preserving the desired properties of interpretability, scalability and power-law behavior, our model is more flexible and provides better predictive performance as illustrated on several datasets.