  The traditional setup of link prediction in networks assumes that a test set
of node pairs, which is usually balanced, is available over which to predict
the presence of links. However, in practice, there is no test set: the
ground-truth is not known, so the number of possible pairs to predict over is
quadratic in the number of nodes in the graph. Moreover, because graphs are
sparse, most of these possible pairs will not be links. Thus, link prediction
methods, which often rely on proximity-preserving embeddings or heuristic
notions of node similarity, face a vast search space, with many pairs that are
in close proximity, but that should not be linked. To mitigate this issue, we
introduce LinkWaldo, a framework for choosing from this quadratic,
massively-skewed search space of node pairs, a concise set of candidate pairs
that, in addition to being in close proximity, also structurally resemble the
observed edges. This allows it to ignore some high-proximity but
low-resemblance pairs, and also identify high-resemblance, lower-proximity
pairs. Our framework is built on a model that theoretically combines Stochastic
Block Models (SBMs) with node proximity models. The block structure of the SBM
maps out where in the search space new links are expected to fall, and the
proximity identifies the most plausible links within these blocks, using
locality sensitive hashing to avoid expensive exhaustive search. LinkWaldo can
use any node representation learning or heuristic definition of proximity, and
can generate candidate pairs for any link prediction method, allowing the
representation power of current and future methods to be realized for link
prediction in practice. We evaluate LinkWaldo on 13 networks across multiple
domains, and show that on average it returns candidate sets containing 7-33%
more missing and future links than both embedding-based and heuristic
baselines' sets.
