Minimax Optimality of Classical Scaling Under General Noise Conditions
This provides theoretical guarantees for a fundamental dimensionality reduction technique under general noise conditions, which is incremental but broadens applicability.
The paper established that classical scaling achieves minimax optimality in recovering true configurations from noisy dissimilarities, requiring only finite fourth moments of noise and deriving matching convergence rates and lower bounds.
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.