  Many prediction problems can be phrased as inferences over local
neighborhoods of graphs. The graph represents the interaction between entities,
and the neighborhood of each entity contains information that allows the
inferences or predictions. We present an approach for applying machine learning
directly to such graph neighborhoods, yielding predicitons for graph nodes on
the basis of the structure of their local neighborhood and the features of the
nodes in it. Our approach allows predictions to be learned directly from
examples, bypassing the step of creating and tuning an inference model or
summarizing the neighborhoods via a fixed set of hand-crafted features. The
approach is based on a multi-level architecture built from Long Short-Term
Memory neural nets (LSTMs); the LSTMs learn how to summarize the neighborhood
from data. We demonstrate the effectiveness of the proposed technique on a
synthetic example and on real-world data related to crowdsourced grading,
Bitcoin transactions, and Wikipedia edit reversions.
