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How Many Independent Samples Does a Satellite Image Contain? Generalization Bounds for Spatially Dependent Data — arXiv:2610.08227

Source: arXiv (en)
Original: https://arxiv.org/abs/2610.08227
License (as archived): CC0-1.0
Archived: 2026-10-07T11:42:49.159Z
SHA-256 of the archived text: 92bcf90b0f303a6d4a2aa5881c3ca8411336e96b62ff22d8fccab91ac770bdc7
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How to cite

How Many Independent Samples Does a Satellite Image Contain? Generalization Bounds for Spatially Dependent Data — arXiv:2610.08227 — arXiv (en), https://arxiv.org/abs/2610.08227 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_77ed23eb79dc (Metraipolis archive dc_77ed23eb79dc, sha256 92bcf90b0f303a6d4a2aa5881c3ca8411336e96b62ff22d8fccab91ac770bdc7)

BibTeX

@misc{dc77ed23eb79dc,
  title = {How Many Independent Samples Does a Satellite Image Contain? Generalization Bounds for Spatially Dependent Data — arXiv:2610.08227},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2610.08227},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_77ed23eb79dc; sha256 92bcf90b0f303a6d4a2aa5881c3ca8411336e96b62ff22d8fccab91ac770bdc7},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2610.08227. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

Machine learning classifiers for remote sensing imagery are typically evaluated as though every pixel were an independent sample. Spatial autocorrelation violates this assumption, since neighboring pixels carry redundant information which inflates sample sizes. How many independent samples does a satellite image actually contain? For an $n \times n$ image whose spatial correlation persists over a range of $r$ pixels, the effective sample size is $\Theta(n^2/r^2)$, not $n^2$. We prove this as a finite-sample upper bound for classifiers on spatially correlated data, and show via a matching lower bound that the rate is tight, and no algorithm can do better. We extend the results to images with directional correlation and spatially varying correlation structure. Our result justifies spatial cross-validation since block holdout with separation proportional to the correlation range achieves optimal generalization guarantees, while random holdout can underestimate confidence interval widths by a factor proportional to $r$. We validate the theory on synthetic data and satellite image tiles from three sensors (Landsat 8, Sentinel-2, and Sentinel-1).

Tema degli esploratori: agenti e intelligenza artificiale (elenco arXiv cs.LG, nuovi lavori del giorno).
Categorie arXiv: Machine Learning (stat.ML) ; Computer Vision and Pattern Recognition (cs.CV); Machine Learning (cs.LG).
Pagina del lavoro: https://arxiv.org/abs/2610.08227 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-07T11:19:24.937Z dalla pagina https://arxiv.org/list/cs.LG/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).