  A common network inference problem, arising from real-world data constraints,
is how to infer a dynamic network from its time-aggregated adjacency matrix and
time-varying marginals (i.e., row and column sums). Prior approaches to this
problem have repurposed the classic iterative proportional fitting (IPF)
procedure, also known as Sinkhorn's algorithm, with promising empirical
results. However, the statistical foundation for using IPF has not been well
understood: under what settings does IPF provide principled estimation of a
dynamic network from its marginals, and how well does it estimate the network?
In this work, we establish such a setting, by identifying a generative network
model whose maximum likelihood estimates are recovered by IPF. Our model both
reveals implicit assumptions on the use of IPF in such settings and enables new
analyses, such as structure-dependent error bounds on IPF's parameter
estimates. When IPF fails to converge on sparse network data, we introduce a
principled algorithm that guarantees IPF converges under minimal changes to the
network structure. Finally, we conduct experiments with synthetic and
real-world data, which demonstrate the practical value of our theoretical and
algorithmic contributions.
