  A variety of machine learning tasks---e.g., matrix factorization, topic
modelling, and feature allocation---can be viewed as learning the parameters of
a probability distribution over bipartite graphs. Recently, a new class of
models for networks, the sparse exchangeable graphs, have been introduced to
resolve some important pathologies of traditional approaches to statistical
network modelling; most notably, the inability to model sparsity (in the
asymptotic sense). The present paper explains some practical insights arising
from this work. We first show how to check if sparsity is relevant for
modelling a given (fixed size) dataset by using network subsampling to identify
a simple signature of sparsity. We discuss the implications of the (sparse)
exchangeable subsampling theory for test-train dataset splitting; we argue
common approaches can lead to biased results, and we propose a principled
alternative. Finally, we study sparse exchangeable Poisson matrix factorization
as a worked example. In particular, we show how to adapt mean field variational
inference to the sparse exchangeable setting, allowing us to scale inference to
huge datasets.
