关于Sparse CCA的支持恢复:信息理论和计算限制
Nilanjana Laha1, Rajarshi Mukherjee2
1Department of Statistics, Texas A&M University, College Station, TX 77843.
IEEE transactions on information theory
|October 16, 2023
概括
我们在高维度正规关联分析 (CCA) 中探索了支恢复. 支持恢复在低稀疏性下是可能的,但在高稀疏性下是不可能的,中度稀疏性显示复杂的计算权衡.
科学领域:
- 统计 统计 统计 统计
- 机器学习 机器学习
- 数据科学数据科学数据科学
背景情况:
- 准则相关性分析 (CCA) 是一种统计方法,用于查找两个变量集之间的关系.
- 高维数据和稀疏结构在统计分析中带来了重大挑战.
- 支持恢复对于识别复杂数据集中的相关变量至关重要.
研究的目的:
- 在高维和稀疏的正规关联分析 (CCA) 中研究非对称的精确支回收.
- 划分不同的稀疏性制度及其对支持恢复的计算和信息理论可行性的影响.
- 建立一致支持恢复的条件,并探索多项式时间算法的极限.
主要方法:
- 信息理论分析,以确定支持回收的下限.
- 开发和分析用于支持恢复的计算效率高的算法.
- 使用坐标值方法和"低度多项式"假设进行计算复杂性分析.
主要成果:
- 确定了四种不同的稀缺性制度,影响支持恢复的可行性.
- 证明支持恢复是可以实现的低稀疏性,但信息理论上不可能高稀疏性.
- 显示的多项式时间恢复在适度稀疏性模式中是可能的,但在更高的适度稀疏性中可能不一致,基于"低度多项式"假设.
结论:
- 在稀疏的CCA中,支持恢复的可行性高度依赖于稀疏程度.
- 在高维设置中支持恢复存在基本限制,受统计和计算因素的影响.
- 该研究提供了对不同稀疏性制度的支持恢复的全面了解,指导了未来的算法开发.
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