从弱依赖数据中进行强大的深度学习.
1Université Jean Monnet, ICJ UMR5208, CNRS, Ecole Centrale de Lyon, INSA Lyon, Universite Claude Bernard Lyon 1, 42023 Saint-Étienne, France.
概括
这项研究引入了强大的深度学习,用于具有无限输出的弱依赖数据. 它为深度神经网络估计器设定了理论界限,在模拟中表现优于传统方法,具有重尾误差.
科学领域:
- 机器学习 机器学习
- 统计 统计 统计 统计
- 深度学习理论 深度学习理论
背景情况:
- 现有的深度学习理论通常假定有界损失函数或数据.
- 这限制了对现实世界场景的适用性,这些场景具有无限变量和重尾分布.
研究的目的:
- 为弱依赖观察开发强大的深度学习理论.
- 为了建立深度神经网络估计器的非对称边界,具有无限制的损失和输出.
- 分析数据时刻顺序 (r) 对估计器性能的影响.
主要方法:
- 在强混合和 ψ-弱依赖下对深度神经网络估计器的理论分析.
- 对预期超额风险的非对称边界的推导.
- 基于霍尔德平滑度和数据时刻属性的收率的研究.
主要成果:
- 建立了强大的深度学习估计器的非对称边界,具有有限的r级时刻 (r>1).
- 当数据具有任何顺序的时刻时,证明的收率接近已知的结果.
- 显示了指数级强烈混合数据方法的速率是i.i.d. 在特定的光滑条件下采样率.
结论:
- 拟议的强大的深度学习框架将理论保证扩展到无限制的数据和损失函数.
- 模拟结果证实了强大的估计器 (绝对和休伯损失) 对回归和自回归中的重尾误差的最小平方的优势.
- 这些发现促进了深度学习在强大的统计建模中的理论理解和实际应用.
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