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Hypothesis Testing in High Dimensions Without Sparsity

无稀疏性的高维假设检验

基本信息

批准号：
1712481
负责人：
Jelena Bradic
金额：
$ 12.5万
依托单位：
University of California-San Diego
依托单位国家：
美国
项目类别：
Continuing Grant
财政年份：
2017
资助国家：
美国
起止时间：
2017-09-01 至 2022-08-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1712481&HistoricalAwards=false
关键词：
Hypothesis Testing Dimensions Without Sparsity

项目摘要

The exponential growth of diverse scientific data represents an unprecedented opportunity to make substantial advances in complex science and engineering, such as the discovery of novel materials or drugs. The collection and analysis of information on massive scales has clear benefits for society: it can help businesses optimize online commerce, medical workers address public health issues, and governments interrupt terrorist activities. This project aims at designing rigorous statistical framework and advanced tools for propagating and managing uncertainty in the modeling and design of complex physical and engineering systems. The ultimate goal of this project is to facilitate significant hypothesis generation and accelerate discovery by correlating data across scientific domains in systems with multi-scale and uncertain parameters in extremely high-dimensional spaces, including for example aerospace, engineering, neuroscience, gene-protein disease networks, materials science, climate science, autonomous systems, and cyber-physical systems or self-organized biological systems. This project will enable the design of systems with verifiable properties; reveal how to value the trustworthiness of results in a wide variety of applications; allow conclusions to be probed for their sensitivity to uncertainties and practical experimentation and validation. Understanding the complex and increasingly data-intensive world around us relies on the construction of robust empirical models, i.e., representations of real, complex systems that enable decision makers to predict behaviors and answer "what-if" questions. Novel statistical research is needed for dealing with the underlying high dimensionality of the space of uncertain parameters, active multi-physics coupling, and uncertainty in the models themselves. Besides, there is no fundamental theory for decision making under uncertainty for these large-scale systems. To address these needs, this project intends to develop the following capabilities: new methods for inverse modeling to scale to high-dimensional multi-scale/multi-physics systems; a quantifiable and generalizable understanding of uncertainties and inadequacies in the physical models themselves and entirely new paradigms for decision making that is extremely robust to model misspecification and assumptions. In particular, new decision theory for high-dimensional regression models will be developed that is highly and provably robust to the model misspecification, including missing, non-sparse and large-scale (exploding) data structures. As such, these methods will be the first attempts at understanding the fundamental limitations of dense high-dimensional models. Moreover, censored analysis models (log-rank, additive hazard, proportional hazard and competing risk) will be studied under the setting where perfect estimation or variable selection is not possible; these studies will be able to bridge the gap between the practice and theory in the high-dimensional setting. Furthermore, a new framework for aggregating heterogeneous and disparate data structures that may be correlated and time-dependent will be developed. The added flexibility in analyzing disparate data going from one stationary source to many moving sources of observations must be carefully balanced with parsimony.

各种科学数据的指数增长代表着在复杂的科学和工程领域取得实质性进展的前所未有的机会，例如发现新材料或药物。大规模信息的收集和分析对社会有明显的好处：它可以帮助企业优化在线商务，医务人员解决公共卫生问题，以及政府中断恐怖活动。该项目旨在设计严格的统计框架和先进的工具，以传播和管理复杂物理和工程系统的建模和设计中的不确定性。该项目的最终目标是通过将具有多尺度和极高维空间中不确定参数的系统中的跨科学领域的数据关联起来，促进重要假设的产生和加速发现，这些系统包括例如航空航天、工程、神经科学、基因-蛋白质疾病网络、材料科学、气候科学、自主系统以及网络物理系统或自组织生物系统。该项目将使系统的设计具有可验证的特性；揭示如何在广泛的应用中评估结果的可信度；允许探讨结论对不确定性的敏感性以及实际实验和验证。理解我们周围日益复杂和数据密集的世界依赖于构建稳健的经验模型，即真实、复杂的系统的表示，使决策者能够预测行为并回答“假设”问题。需要新的统计研究来处理不确定参数空间的高维、活跃的多物理耦合以及模型本身的不确定性。此外，对于这些大系统，在不确定条件下的决策也没有基础理论。为了满足这些需要，该项目打算开发以下能力：新的逆建模方法，以适应高维多尺度/多物理系统；对物理模型本身的不确定性和不足之处的可量化和可概括的理解；以及对模型错误说明和假设极其稳健的全新决策范例。特别是，高维回归模型的新决策理论将被开发出来，它对模型错误指定具有高度和可证明的健壮性，包括丢失、非稀疏和大规模(爆炸)数据结构。因此，这些方法将是理解密集高维模型的根本局限性的第一次尝试。此外，删失分析模型(对数等级、加性风险、比例风险和竞争风险)将在不可能进行完美估计或变量选择的情况下进行研究；这些研究将能够在高维环境下弥合实践与理论之间的差距。此外，还将开发一个新的框架，用于聚合可能相互关联且与时间相关的异类和不同的数据结构。在分析从一个固定观测来源到多个移动观测来源的不同数据时增加的灵活性必须与简约谨慎地平衡。