Conditional Modeling and Conditional Inference

条件建模和条件推理

• 批准号: 1007593
• 负责人: Stuart Geman
• 金额: $ 24.6万
• 依托单位: Brown University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2010
• 资助国家: 美国
• 起止时间: 2010-09-15 至 2013-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1007593&HistoricalAwards=false
• 关键词: Conditional; Modeling; Inference

In many applications, the complexity and dimensionality of the data preclude nonparametric inference, despite the availability of massive data sets. At the same time, it is usually true that too little is known about the detailed mechanisms generating the data to meaningfully specify parametric models. Conditional modeling and conditional inference are semi-parametric approaches to complex high-dimensional data in which attention is focused on manageable low-dimensional statistical modeling and estimation. Applications include efficient feature estimation and data classification (e.g. in computer vision), exact tests for broad and scientifically relevant hypotheses (e.g. in the statistical analysis of multi-electrode neuronal recordings), exploration of time scale in non-stationary processes (e.g. in the study of market dynamics), and construction of complex distributions through successive low-dimensional perturbations (e.g. in the study of probabilistic context-sensitive grammars). High-dimensional data are ubiquitous. Sources include molecular biology, finance, neurophysiological recordings, and the imagery and text of the Internet. Despite the availability of almost unlimited amounts of these data, their complexity and high dimensionality challenge existing statistical models and represent a bottleneck to successful applications. Oftentimes the complexity and dimensionality can be finessed through mathematical methods that select and focus on a collection of low-dimensional characteristics of the data. The approach avoids untenable or un-testable model assumptions without necessarily compromising the information content and power of the data. The research is at the interface between statistical theory and scientific application, with potential impact in technology (e.g. through computer vision) and, more broadly, society (e.g. through neuroscience and better financial modeling).

在许多应用中，尽管有大量的数据集，但数据的复杂性和维度排除了非参数推理的可能性。同时，人们通常对生成数据的详细机制知之甚少，无法有意义地指定参数模型。条件建模和条件推理是对复杂高维数据的半参数方法，其中的注意力集中在可管理的低维统计建模和估计上。应用包括有效的特征估计和数据分类(例如在计算机视觉中)，对广泛的和科学上相关的假设的精确测试(例如在多电极神经元记录的统计分析中)，探索非平稳过程中的时间尺度(例如在市场动力学研究中)，以及通过连续的低维扰动构造复杂分布(例如在概率上下文敏感语法的研究中)。高维数据无处不在。来源包括分子生物学、金融、神经生理学记录以及互联网的图像和文本。尽管这些数据几乎是无限的，但它们的复杂性和高维性挑战了现有的统计模型，并成为成功应用的瓶颈。通常，可以通过选择并集中于数据的低维特征集合的数学方法来精细化复杂性和维度。该方法避免了不成立或不可检验的模型假设，而不一定会损害数据的信息内容和能力。这项研究处于统计理论和科学应用之间的交界处，对技术(例如通过计算机视觉)以及更广泛的社会(例如通过神经科学和更好的金融建模)具有潜在的影响。