  In many retrieval problems, where we must retrieve one or more entries from a
gallery in response to a probe, it is common practice to learn to do by
directly comparing the probe and gallery entries to one another. In many
situations the gallery and probe have common covariates -- external variables
that are common to both. In principle it is possible to perform the retrieval
based merely on these covariates. The process, however, becomes gated by our
ability to recognize the covariates for the probe and gallery entries
correctly.
  In this paper we analyze optimal strategies for retrieval based only on
matching covariates, when the recognition of the covariates is itself
inaccurate. We investigate multiple problems: recovering one item from a
gallery of $N$ entries, matching pairs of instances, and retrieval from large
collections. We verify our analytical formulae through experiments to verify
their correctness in practical settings.
