mlsanityData to 14 Oct 2026

Adaptive Metric Dimensionality Reduction

arXiv 1302.2752 ↗First posted 12 Feb 2013cs.LG cs.DS stat.MLcited by 14

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Abstract (arXiv)

We study adaptive data-dependent dimensionality reduction in the context of supervised learning in general metric spaces. Our main statistical contribution is a generalization bound for Lipschitz functions in metric spaces that are doubling, or nearly doubling. On the algorithmic front, we describe an analogue of PCA for metric spaces: namely an efficient procedure that approximates the data's intrinsic dimension, which is often much lower than the ambient dimension. Our approach thus leverages the dual benefits of low dimensionality: (1) more efficient algorithms, e.g., for proximity search, and (2) more optimistic generalization bounds.

Key facts. Cited by 14 papers in the map (data through 14 Oct 2026). First posted on arXiv 12 Feb 2013.

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Citing papers per year: 2021: 1; 2022: 2; 2023: 6; 2024: 3; 2025: 1; 2026: 1.

14 papers.

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  1. 2023Out-of-distributional risk bounds for neural operators with applications to the Helmholtz equationcited by 32
  2. 2021Intrinsic Dimension Estimation Using Wasserstein Distancescited by 20
  3. 2023Covariate balancing using the integral probability metric for causal inferencecited by 9
  4. 2023Covering Number of Real Algebraic Varieties and Beyond: Improved Bounds and Applicationscited by 8
  5. 2023Optimal Scalarizations for Sublinear Hypervolume Regretcited by 7
  6. 2023Near-optimal learning with average H"older smoothnesscited by 4
  7. 2024Trustworthy Actionable Perturbationscited by 3
  8. 2025Private Evolution Convergescited by 2
  9. 2022Teacher Guided Training: An Efficient Framework for Knowledge Transfercited by 1
  10. 2023Efficient Agnostic Learning with Average Smoothnesscited by 1
  11. 2026Variational Entropic Optimal Transportcited by 1
  12. 2022Non-Linear Spectral Dimensionality Reduction Under Uncertaintycited by 0
2 more
  1. 2024Tighter Learning Guarantees on Digital Computers via Concentration of Measure on Finite Spacescited by 0
  2. 2024Fine-Grained Uncertainty Quantification via Collisionscited by 0