We consider the problem of learning the nearest neighbor graph of a dataset
of n items. The metric is unknown, but we can query an oracle to obtain a noisy
estimate of the distance between any pair of items. This framework applies to
problem domains where one wants to learn people's preferences from responses
commonly modeled as noisy distance judgments. In this paper, we propose an
active algorithm to find the graph with high probability and analyze its query
complexity. In contrast to existing work that forces Euclidean structure, our
method is valid for general metrics, assuming only symmetry and the triangle
inequality. Furthermore, we demonstrate efficiency of our method empirically
and theoretically, needing only O(n log(n)Delta^-2) queries in favorable
settings, where Delta^-2 accounts for the effect of noise. Using crowd-sourced
data collected for a subset of the UT Zappos50K dataset, we apply our algorithm
to learn which shoes people believe are most similar and show that it beats
both an active baseline and ordinal embedding.Comment: 21 total pages (8 main pages + appendices), 7 figures, submitted to
NeurIPS 201