CAREER: Geometric approaches to hierarchical and nonparametric model-based inference
职业:基于分层和非参数模型的推理的几何方法
基本信息
- 批准号:1351362
- 负责人:
- 金额:$ 40万
- 依托单位:
- 依托单位国家:美国
- 项目类别:Continuing Grant
- 财政年份:2014
- 资助国家:美国
- 起止时间:2014-07-01 至 2020-06-30
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
Hierarchical and nonparametric models present some of the most fundamental and powerful tools in modern statistics. Despite valuable advances made in the past decades, there are several widely recognized and emerging problems. First, even as these models are increasingly applied to large data sets and complex domains, a statistical theory for inferential behaviors of the hierarchy of latent variables present in the models is not yet available. Second, local inference methods based on sampling, although simple to derive, tend to converge too slowly, thereby losing their effectiveness. Third, most existing methods are incapable of handling highly distributed data sources, which are increasingly responsible for the influx of big data. Addressing these challenges requires fundamentally new ideas in theory, modeling and algorithms that must account for the contrast and interplay between the global geometry of an inference problem and the need for decentralization of inference and algorithmic implementation. This project aims to make fundamental contributions toward advancing hierarchical model-based inference. They include a statistical theory for the latent hierarchy of variables and for analyzing the effects of transfer learning. They also include variational inference algorithms based on the global geometry of latent structures and geometric analyses of the tradeoffs between statistical and computational efficiencies. Both the algorithms and theory are unified by the use of Wasserstein geometry, which arises from the mathematical theory of optimal transportation. Moreover, scalable hierarchical models will be developed that can exploit highly distributed data sources and decentralized inference architectures.This research will improve our ability to manage, analyze and make decisions with large-scale, high dimensional and complex data, especially in the research and applications of networks and the environment. The decentralized detection algorithms for highly distributed data sources have the potential of advancing the state of the art technologies that support data-driven and high-performance distributed computing architectures. As such, this research has the potential of extending the capabilities of the real-time detection and tracking devices currently deployed in the health-care and security domains. The optimal transport based theory will deepen our understanding of hierarchical Bayesian inference, a fundamental concept of modern statistics. The algorithms and geometric analyses will provide useful tradeoffs between statistical and computational complexity, an important issue lying in the interface of Statistics and Computer Science. This research will also provide support for broadening the current statistics curriculum at the University of Michigan. The PI will integrate the teaching of statistical and computational tools with modern applications, by developing synthesis courses which interact closely with research topics of the project. This provides an excellent opportunity to train students with a broad base of knowledge and cross-disciplinary skills in the fields of statistics, probability, machine learning, distributed computation and networked systems.
分层模型和非参数模型提供了现代统计学中一些最基本和最强大的工具。尽管过去几十年取得了宝贵的进步,但仍存在一些广泛认识到的和正在出现的问题。首先,即使这些模型越来越多地应用于大型数据集和复杂领域,但模型中存在的潜在变量层次结构的推理行为的统计理论尚不可用。其次,基于采样的局部推理方法虽然推导简单,但往往收敛速度太慢,从而失去有效性。第三,大多数现有方法无法处理高度分布式的数据源,而这些数据源日益成为大数据涌入的原因。解决这些挑战需要在理论、建模和算法方面从根本上提出新的想法,这些想法必须考虑推理问题的全局几何结构与推理和算法实现的去中心化需求之间的对比和相互作用。 该项目旨在为推进基于分层模型的推理做出基础贡献。它们包括用于变量潜在层次结构和分析迁移学习效果的统计理论。它们还包括基于潜在结构的全局几何的变分推理算法以及统计和计算效率之间权衡的几何分析。算法和理论都通过 Wasserstein 几何学的使用统一起来,该几何学源于最优交通的数学理论。 此外,将开发可扩展的层次模型,可以利用高度分布式的数据源和去中心化的推理架构。这项研究将提高我们对大规模、高维和复杂数据进行管理、分析和决策的能力,特别是在网络和环境的研究和应用方面。针对高度分布式数据源的分散检测算法有可能推动支持数据驱动和高性能分布式计算架构的最先进技术。因此,这项研究有可能扩展目前在医疗保健和安全领域部署的实时检测和跟踪设备的功能。基于最优传输的理论将加深我们对分层贝叶斯推理(现代统计学的基本概念)的理解。算法和几何分析将在统计和计算复杂性之间提供有用的权衡,这是统计和计算机科学接口中的一个重要问题。这项研究还将为扩大密歇根大学当前的统计课程提供支持。 PI 将通过开发与项目研究主题密切互动的综合课程,将统计和计算工具的教学与现代应用相结合。 这为培养学生在统计、概率、机器学习、分布式计算和网络系统领域拥有广泛的知识基础和跨学科技能提供了绝佳的机会。
项目成果
期刊论文数量(0)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
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Xuanlong Nguyen其他文献
Xuanlong Nguyen的其他文献
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{{ truncateString('Xuanlong Nguyen', 18)}}的其他基金
Parameter Estimation Theory and Algorithms under Latent Variable Models and Model Misspecification
潜变量模型和模型错误指定下的参数估计理论和算法
- 批准号:
2015361 - 财政年份:2020
- 资助金额:
$ 40万 - 项目类别:
Standard Grant
TWC: Medium: Collaborative: Data is Social: Exploiting Data Relationships to Detect Insider Attacks
TWC:媒介:协作:数据是社交的:利用数据关系检测内部攻击
- 批准号:
1409303 - 财政年份:2014
- 资助金额:
$ 40万 - 项目类别:
Standard Grant
CIF: Collaborative Research:Small: Distributed Detection Algorithms and Stochastic Modeling for Large Monitoring Sensor Networks
CIF:协作研究:小型:大型监控传感器网络的分布式检测算法和随机建模
- 批准号:
1115769 - 财政年份:2011
- 资助金额:
$ 40万 - 项目类别:
Standard Grant
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