  Recently, learning with soft labels has been shown to achieve better
performance than learning with hard labels in terms of model generalization,
calibration, and robustness. However, collecting pointwise labeling confidence
for all training examples can be challenging and time-consuming in real-world
scenarios. This paper delves into a novel weakly supervised binary
classification problem called confidence-difference (ConfDiff) classification.
Instead of pointwise labeling confidence, we are given only unlabeled data
pairs with confidence difference that specifies the difference in the
probabilities of being positive. We propose a risk-consistent approach to
tackle this problem and show that the estimation error bound achieves the
optimal convergence rate. We also introduce a risk correction approach to
mitigate overfitting problems, whose consistency and convergence rate are also
proven. Extensive experiments on benchmark data sets and a real-world
recommender system data set validate the effectiveness of our proposed
approaches in exploiting the supervision information of the confidence
difference.
