  As graph data becomes more ubiquitous, the need for robust inferential graph
algorithms to operate in these complex data domains is crucial. In many cases
of interest, inference is further complicated by the presence of adversarial
data contamination. The effect of the adversary is frequently to change the
data distribution in ways that negatively affect statistical and algorithmic
performance. We study this phenomenon in the context of vertex nomination, a
semi-supervised information retrieval task for network data. Here, a common
suite of methods relies on spectral graph embeddings, which have been shown to
provide both good algorithmic performance and flexible settings in which
regularization techniques can be implemented to help mitigate the effect of an
adversary. Many current regularization methods rely on direct network trimming
to effectively excise the adversarial contamination, although this direct
trimming often gives rise to complicated dependency structures in the resulting
graph. We propose a new trimming method that operates in model space which can
address both block structure contamination and white noise contamination
(contamination whose distribution is unknown). This model trimming is more
amenable to theoretical analysis while also demonstrating superior performance
in a number of simulations, compared to direct trimming.
