Label differential privacy (DP) is a framework that protects the privacy of
labels in training datasets, while the feature vectors are public. Existing
approaches protect the privacy of labels by flipping them randomly, and then
train a model to make the output approximate the privatized label. However, as
the number of classes $K$ increases, stronger randomization is needed, thus the
performances of these methods become significantly worse. In this paper, we
propose a vector approximation approach, which is easy to implement and
introduces little additional computational overhead. Instead of flipping each
label into a single scalar, our method converts each label into a random vector
with $K$ components, whose expectations reflect class conditional
probabilities. Intuitively, vector approximation retains more information than
scalar labels. A brief theoretical analysis shows that the performance of our
method only decays slightly with $K$. Finally, we conduct experiments on both
synthesized and real datasets, which validate our theoretical analysis as well
as the practical performance of our method.

我们提出了一种向量逼近方法，将每个标签转换成具有 K 个分量的随机向量，其期望值反映类别条件概率，该方法在理论上只略微下降，并通过实验证实了我们的理论分析和方法的实际性能。