Theory and practice of nonparametric detection

非参数检测的理论与实践

• 批准号: 0603890
• 负责人: Ery Arias-Castro
• 金额: $ 12万
• 依托单位: University of California-San Diego
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2006
• 资助国家: 美国
• 起止时间: 2006-07-01 至 2011-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0603890&HistoricalAwards=false
• 关键词: Theory; practice; nonparametric; detection

The scan statistic, or matched filter, has been extensively used for detection tasks. In many instances, a parametric model is assumed for simplicity and computational limitations. Also, various parametric settings for detection have been studied over the years. In particular, the investigator has done a study that establishes minimax rates for a large variety of problems and proves that the scan statistic achieves the optimal rate. However, most detection problems are nonparametric in nature, making it important to gain similar insight into nonparametric detection problems. By studying the problem of detection on graphs and drawing connections with Statistical Mechanics, the investigator brings a new understanding of such problems. The investigator also designs flexible graphical structures based on multiscale ideas to be the corner stone for developing new tools in various applied settings.The problem of detection arises in a wide variety of settings such as in analyzing galaxy catalogs; object tracking; road tracking; satellite imagery, which includes detecting man-made objects, detecting ships and fires; environment monitoring, which includes controlling pollution levels of water sources, detection of disease outbreaks and detection/localization of whales in the Ocean from acoustic data. The investigator studies the theoretical properties of the scan statistic in more complex (nonparametric) models for such detection tasks. Though the scan statistic has been extensively used in virtually all such problems, its behavior is mostly known under rather simplified (parametric) assumptions. Further, the investigator develops new tools for implementing the scan statistic in such complex detection settings. Such efficient tools are currently needed in many Scientific and Engineering fields, such as Astrophysics, in detecting galaxy clusters.

扫描统计，或匹配滤波器，已被广泛用于检测任务。在许多情况下，为了简单和计算限制，假设参数模型。此外，多年来已经研究了用于检测的各种参数设置。特别是，研究人员已经做了一项研究，建立了极大极小率的各种问题，并证明了扫描统计达到最佳率。然而，大多数检测问题本质上是非参数的，因此获得类似的非参数检测问题的洞察力非常重要。通过对图上检测问题的研究，并将其与统计力学联系起来，使人们对这类问题有了新的认识。 研究人员还设计了灵活的图形结构的基础上多尺度的想法是基石开发新的工具，在各种应用设置检测的问题出现在各种各样的设置，如分析星系目录;对象跟踪;道路跟踪;卫星图像，其中包括检测人造物体，检测船舶和火灾;环境监测，包括控制水源污染程度、检测疾病爆发和根据声学数据检测/定位海洋中的鲸鱼。调查研究的理论性质的扫描统计在更复杂的（非参数）模型，这样的检测任务。 虽然扫描统计量已被广泛用于几乎所有此类问题，其行为大多是已知的，而简化（参数）的假设。此外，研究人员开发了新的工具，用于在这种复杂的检测设置中实现扫描统计。这种有效的工具是目前需要在许多科学和工程领域，如天体物理学，在检测星系团。