与多拉普拉斯图的回归的收率.
Nicolás García Trillos1, Ryan Murray2, Matthew Thorpe3
1Department of Statistics, University of Wisconsin-Madison, Madison, WI 53706 USA.
Sampling theory, signal processing, and data analysis
|December 1, 2023
概括
这项研究引入了非参数回归的图形聚拉普拉斯规范化. 它在一个大数据极限中识别了光滑函数与真函数的收率,显示了与传统光滑线相比的有希望的结果.
科学领域:
- 机器学习 机器学习
- 图形信号处理 图形信号处理
- 统计学学习理论
背景情况:
- 平滑线条是非参数回归的标准工具,利用拉普拉斯规则化来实现平滑.
- 使用聚拉普拉斯规范化可以实现更高阶的规律性,扩展传统方法的功能.
- 将这些规范化技术适应于图形结构数据对于分析复杂网络至关重要.
研究的目的:
- 在完全监督的非参数回归设置中研究图形聚拉普拉西安调节的应用.
- 在大数据极限中分析拟议方法对杂图形数据的收率.
- 为了比较图形多拉普拉斯规则化的性能与标准光滑线条模型.
主要方法:
- 制定一个变量问题,最小化一个由数据忠实性和图形多拉普拉斯式项组成的能量函数.
- 考虑一个带有噪音标签的数据集,并将该方法应用于几何随机图.
- 在独立且相同分布 (i.i.d.) 条件下分析最小化器与真实底层函数的收率. 噪音假设. 噪音假设.
主要成果:
- 该研究以很高的概率确定了估计函数与真函数的收率.
- 这种收率是在大数据极限 (N → ∞) 中建立的.
- 演算的收率被证明与标准光滑线模型的已知率相比较.
结论:
- 图形多拉普拉斯规范化是一种可行且有效的方法,用于对图形结构数据进行非参数回归.
- 该方法提供了对收率的理论保证,特别是在存在噪音和大型数据集的情况下.
- 这些发现表明,图形的多拉普拉斯规则化为图形数据分析提供了光滑斜线的强大延伸.
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