arXiv：cs.LG· Robin Young·· 6 小时前AI 评分44
一张卫星图像包含多少独立样本？空间相关数据的泛化边界
How Many Independent Samples Does a Satellite Image Contain? Generalization Bounds for Spatially Dependent Data
AI 导读
研究证明，对于空间相关性持续范围为 r 像素的 n×n 图像，有效样本量为 Θ(n²/r²) 而非 n²，并给出匹配下界证明该速率是紧的。该结果支持空间交叉验证：相关性范围成比例的块留出可达最优泛化保证，而随机留出会将置信区间宽度低估约 r 倍。理论在合成数据及 Landsat 8、Sentinel-2、Sentinel-1 三种传感器的卫星图像瓦片上得到验证。
正文
Abstract: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).
| Subjects: | Machine Learning (stat.ML); Computer Vision and Pattern Recognition (cs.CV); Machine Learning (cs.LG) |
| Cite as: | arXiv:2610.08227 [stat.ML] |
| (or arXiv:2610.08227v1 [stat.ML] for this version) | |
| https://doi.org/10.48550/arXiv.2610.08227 arXiv-issued DOI via DataCite (pending registration) |
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| Journal reference: | IEEE Transactions on Geoscience and Remote Sensing (2026) vol. 64 |
| Related DOI: | https://doi.org/10.1109/TGRS.2026.3739158
DOI(s) linking to related resources |
Submission history
From: Robin Young [view email]
[v1]
Tue, 6 Oct 2026 12:14:34 UTC (530 KB)
来源：arXiv：cs.LG · arxiv.org