Construction and Analysis of Methods for Making Appropriate Use of Low Dimensional Structure in Data and Models When Apparent Dimension is Very High

表观维数很高时在数据和模型中适当使用低维结构的方法的构建和分析

• 批准号: 0605236
• 负责人: Peter Bickel
• 金额: $ 45万
• 依托单位: University of California-Berkeley
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2006
• 资助国家: 美国
• 起止时间: 2006-07-15 至 2010-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0605236&HistoricalAwards=false
• 关键词: Construction; Analysis; Methods; Making; Appropriate

The investigator develops and analyzes asymptotically methods for inference and prediction for high dimensional data. His research with collaborators includes estimation of intrinsic dimension, estimation of high dimensional covariance matrices and prediction using low dimensional approximate representations of the data and/ or approximate low dimensional models.The goal of the investigators research is to improve prediction and inference in situations ranging from numerical weather prediction to computational biology when high dimensional data is the basis of action and understanding. In fact, such data nowadays arise everywhere. The underlying principle the investigator and collaborators are following is that the data is essentially low dimensional when properly represented and/or modeled and that appropriate representations can be found in computationally feasible ways.

研究者开发并分析了高维数据的渐近推理和预测方法。他与合作者的研究包括内在维度的估计、高维协方差矩阵的估计以及使用数据的低维近似表示和/或近似低维模型进行预测。研究人员研究的目标是在高维数据为基础的情况下，改善从数值天气预报到计算生物学的预测和推断 行动和理解。事实上，如今这样的数据随处可见。研究者和合作者遵循的基本原则是，数据在适当表示和/或建模时基本上是低维的，并且可以以计算上可行的方式找到适当的表示。