This paper provides theoretical insights into high-dimensional binary
classification with class-conditional noisy labels. Specifically, we study the
behavior of a linear classifier with a label noisiness aware loss function,
when both the dimension of data $p$ and the sample size $n$ are large and
comparable. Relying on random matrix theory by supposing a Gaussian mixture
data model, the performance of the linear classifier when $p,n\to \infty$ is
shown to converge towards a limit, involving scalar statistics of the data.
Importantly, our findings show that the low-dimensional intuitions to handle
label noise do not hold in high-dimension, in the sense that the optimal
classifier in low-dimension dramatically fails in high-dimension. Based on our
derivations, we design an optimized method that is shown to be provably more
efficient in handling noisy labels in high dimensions. Our theoretical
conclusions are further confirmed by experiments on real datasets, where we
show that our optimized approach outperforms the considered baselines.

该研究论文探讨了高维二分类在具有条件性噪声标签的情况下的理论视角。通过研究具有标签噪声感知损失函数的线性分类器在维度 p 和样本数 n 都很大且可比时的行为，利用随机矩阵理论和高斯混合数据模型，证明了当 p 和 n 趋近于无穷时，线性分类器的性能收敛至涉及数据的标量统计量的一个界限。重要的是，我们的发现表明低维处理标签噪声的直觉在高维中不成立，即低维中的最优分类器在高维中出现显著失败。基于我们的推导，我们设计了一种优化方法，经证明在处理高维噪声标签方面更加高效。我们的理论结论在真实数据集上的实验证实了我们的优化方法优于考虑的基准方法。