对于高斯过程的可证明准确的可扩展近似的辐射邻居
Yichen Zhu1, Michele Peruzzi2, Cheng Li3
1Bocconi Institute for Data Science and Analytics, Bocconi University, Milan, MI, Italy.
Biometrika
|April 14, 2025
概括
辐射邻居高斯过程 (RadGP) 提供了一个理论上验证的方法,用于在大数据集中近似高斯过程. 这种方法确保了准确的近似,提高了地理统计分析的可扩展性和图形模型规格.
科学领域:
- 地质统计学 在地质统计学
- 计算统计学 计算统计学
- 机器学习 机器学习
背景情况:
- 高斯过程 (GPs) 是空间建模的强大工具,但面临着大量数据集的计算挑战.
- 现有的稀疏定向非循环图 (DAG) 近似方法缺乏理论保证,导致模型规范和对图形结构的敏感性存在困难.
- 在地球统计学中,需要可扩展和理论上的GP近似值.
研究的目的:
- 介绍辐射邻居高斯过程 (RadGP) 作为基于DAG的GP近似的新型类.
- 提供RadGP在接近不受限制的全科医生的准确性方面的理论验证.
- 在地理统计应用中展示RadGP的实用实用性.
主要方法:
- 开发了一种新的DAG结构,其中节点连接到定义半径内的邻居.
- 制定了RadGP作为一个特定的类别的稀疏的DAG近似的GPs.
- 使用瓦瑟斯坦-2距离证明了理论近似界限.
主要成果:
- 证明RadGP准确地接近不受限制的全科医生.
- 建立了一个取决于近似半径,共变函数和样本分散的错误率.
- 在模拟和真实数据上的前后近似中表现出色.
结论:
- RadGP为现有的GP近似方法提供了理论上合理且可扩展的替代方案.
- 该方法为图形模型规范提供了明确的指导,并减少了对图形选择的敏感性.
- 对于大规模的地理统计问题,RadGP是有效的,增强了前后推理.
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