Uncoupled Regression from Pairwise Comparison Data

TL;DR

This paper introduces a novel framework for uncoupled regression using pairwise comparison data, enabling model learning without strong assumptions and preserving data anonymity, with proven convergence and competitive empirical results.

Contribution

The paper presents a new approach to uncoupled regression that leverages pairwise comparison data, avoiding restrictive assumptions and ensuring convergence to the optimal model.

Findings

Methods converge to the optimal model with uniform target distribution.

Proposed methods perform comparably to supervised regression on linear models.

Framework preserves data anonymity while enabling effective regression.

Abstract

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.