and shown that our approach outperforms competing models in link prediction. The model could be extended in several directions. One could consider asymmetry in the base intensities $\mu_{ij}\neq \mu_{ji}$ and/or a bilinear form as in [@Zhou2015]. Another important extension would be the estimation of the number of latent commmunities/features $p$.

**Acknowledgments.** The authors thank the reviewers and area chair for their constructive comments. XM, FC and YWT acknowledge funding from the ERC under the European Union’s 7th Framework programme (FP7/2007-2013) ERC grant agreement no. 617071. FC acknowledges support from EPSRC under grant EP/P026753/1 and from the Alan Turing Institute under EPSRC grant EP/N510129/1. XM acknowledges support from the A. G. Leventis Foundation.

Supplementary Material {#supplementary-material .unnumbered}
======================

A: Background on compound completely random measures {#a-background-on-compound-completely-random-measures .unnumbered}
====================================================

We give the necessary background on compound completely random measures (CCRM). An extensive account of this class of models is given in [@Griffin2017]. In this article, we consider a CCRM $(W_1,\ldots,W_p)$ on $\mathbb R_+$ characterized, for any $(t_1,\ldots,t_p)\in\mathbb R_+^p$ and measurable set $A\subset \mathbb R_+$, by $$\mathbb E[e^{-\sum_{k=1}^p t_k W_k(A)}] =\exp (-H_0(A)\psi(t_1,\ldots,t_p))$$ where $H_0$ is the Lebesgue measure and $\psi$ is the multivariate Laplace exponent defined by $$\psi(t_1,\ldots,t_p)  = \int_{\mathbb{R}^p_+}(1-e^{-\sum_{k=1}^p t_k w_k})\rho(dw_{1},\ldots,dw_p).
\label{eq:laplaceexponent}$$ 