Uncoupled Regression from Pairwise Comparison Data
This addresses the challenge of learning from anonymized data, such as sensitive income information, without breaking anonymity, though it is incremental as it builds on existing uncoupled regression methods by relaxing assumptions.
The paper tackles the problem of uncoupled regression, where the correspondence between data points and target values is unknown, by introducing a framework that uses pairwise comparison data to learn a model without strong assumptions on the true target function. The result shows that the learned model converges optimally under uniform distribution and is empirically comparable to supervised regression for linear models.
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.