Nonparametric Prediction and Structure Discovery for Spatial Dynamics

空间动力学的非参数预测和结构发现

• 批准号: 1207759
• 负责人: Cosma Shalizi
• 金额: $ 18万
• 依托单位: Carnegie-Mellon University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2012
• 资助国家: 美国
• 起止时间: 2012-09-01 至 2015-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1207759&HistoricalAwards=false
• 关键词: Nonparametric; Prediction; Structure; Discovery; Spatial

This project develops new methods for non-parametric prediction, filtering, and structure discovery, primarily for spatio-temporal data but also in a range of other settings with high-dimensional observations, such as networks. There are two novel aspects to the investigation's approach. First, rather than trying to predict spatio-temporal data globally, or according to a fixed pattern, it exploits the dynamics of the system to develop a novel form of local prediction which still captures long-scale structure. Second, while conventional non-parametric smoothing is based on the usual geometry of the space of predictor variables, this is supplemented smoothing together input points which have similar predictive consequences, in effect discovering a new geometry. This approach, which draws on earlier work on information theory in nonlinear dynamics, allows for accurate forecasting of the evolution of large spatio-temporal systems in a computationally efficient manner. It also allows for the automatic discovery of complex higher-level structures in such data. Scientific data increasingly comes as complex measurements spread over space and time. Scientists need ways to forecast how such systems will evolve, and to automatically separate important (but perhaps subtle) patterns from inconsequential "background" of the system, since the structures are often crucial to understanding the dynamics. This project tackles both of these challenging statistical problems together. It combines idea from information theory and nonlinear physics with modern tools of flexible statistical modeling to discover the intrinsic dynamics of the system from the data itself, and uses these structures for both prediction and filtering. Areas of potential application include neuroscience, fluid dynamics, and ecology, where it would help forecast the behavior of complex systems, and help to find the organized structures which are keys to controlling that behavior.

该项目开发了用于非参数预测，过滤和结构发现的新方法，主要用于时空数据，但也用于具有高维观测的其他设置，如网络。 调查方法有两个新颖的方面。 首先，它不是试图预测全球的时空数据，或根据一个固定的模式，它利用系统的动态发展一种新形式的本地预测，仍然捕捉长期的结构。 其次，虽然传统的非参数平滑是基于预测变量空间的通常几何形状，但这是补充平滑具有类似预测结果的输入点，实际上发现了一个新的几何形状。 这种方法，它借鉴了非线性动力学信息理论的早期工作，允许精确预测的大型时空系统的演化在计算上有效的方式。 它还允许自动发现此类数据中复杂的高级结构。科学数据越来越多地来自跨越空间和时间的复杂测量。 科学家们需要一些方法来预测这样的系统将如何演变，并自动将重要的（但可能是微妙的）模式从系统的无关紧要的“背景”中分离出来，因为结构通常对理解动态至关重要。 这个项目同时解决了这两个具有挑战性的统计问题。 它将信息论和非线性物理学的思想与灵活的统计建模的现代工具相结合，从数据本身发现系统的内在动力学，并使用这些结构进行预测和过滤。 潜在的应用领域包括神经科学，流体动力学和生态学，它将有助于预测复杂系统的行为，并有助于找到控制该行为的关键组织结构。