在广泛噪声下证明经典尺度法最优，仅需四阶矩有限。
Minimax Optimality of Classical Scaling Under General Noise Conditions
- 仅需噪声四阶矩有限，放宽传统假设。
- 推导收敛速率并证明其达最小最大下界。
- 适合关注降维鲁棒性与理论保证的研究者。
我们建立了经典尺度法在一大类噪声模型下的相合性，涵盖文献中许多常见情形。该方法仅需噪声具有有限四阶矩，显著弱化了标准假设。我们推导出经典尺度法的收敛速率，并建立匹配的最小最大下界，证明即使输入相异度受噪声污染，经典尺度法仍能实现真实构型恢复的最小最大最优性。
原文摘要 · Abstract (English)
We establish the consistency of classical scaling under a broad class of noise models, encompassing many commonly studied cases in literature. Our approach requires only finite fourth moments of the noise, significantly weakening standard assumptions. We derive convergence rates for classical scaling and establish matching minimax lower bounds, demonstrating that classical scaling achieves minimax optimality in recovering the true configuration even when the input dissimilarities are corrupted by noise.
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