在稀疏的非参数模型中进行自适应精确回收
Natalia Stepanova1, Marie Turcicova2
1School of Mathematics and Statistics, Carleton University, 1125 Colonel By Drive, K1S 5B6 Ottawa, ON Canada.
概括
这项研究确定了高维模型中未知函数的非零元件. 一种新的选择程序实现了精确的变量选择,适应模型稀疏性.
科学领域:
- 统计 统计 统计 统计
- 机器学习 机器学习
- 高维数据分析 高维数据分析
背景情况:
- 在高斯白噪声模型中观察一个未知函数f (t) 的d变量.
- 假设f (t) 是k变量函数 (1 <= k <= s) 的和,只有少数函数不等于零.
- 在高维环境中解决挑战,d ->无限和s也可以成长.
研究的目的:
- 确定未知函数 f (t) 的非零元件.
- 为日益复杂的高维模型开发一个可变选择程序.
- 为了确定成功和不可能的确切变量选择的条件.
主要方法:
- 使用高斯白噪声模型,强度epsilon>0.
- 开发一个适应模型稀疏性 (参数β) 的变量选择程序.
- 导出准确的变量选择的理论条件.
主要成果:
- 确定的条件,在这些条件下,可以选择精确的变量.
- 提出了一种适应性选择程序,可以实现精确的变量选择.
- 识别了排除精确变量选择的条件.
结论:
- 开发的程序允许在高维,稀疏的设置中精确选择变量.
- 这些发现为理解变量选择限制提供了一个理论框架.
- 这项工作推进了复杂模型的统计推理领域.
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