  Uncoupled regression is the problem to learn a model from unlabeled data and
the set of target values while the correspondence between them is unknown. Such
a situation arises in predicting anonymized targets that involve sensitive
information, e.g., one's annual income. Since existing methods for uncoupled
regression often require strong assumptions on the true target function, and
thus, their range of applications is limited, we introduce a novel framework
that does not require such assumptions in this paper. Our key idea is to
utilize pairwise comparison data, which consists of pairs of unlabeled data
that we know which one has a larger target value. Such pairwise comparison data
is easy to collect, as typically discussed in the learning-to-rank scenario,
and does not break the anonymity of data. We propose two practical methods for
uncoupled regression from pairwise comparison data and show that the learned
regression model converges to the optimal model with the optimal parametric
convergence rate when the target variable distributes uniformly. Moreover, we
empirically show that for linear models the proposed methods are comparable to
ordinary supervised regression with labeled data.
