New Challenges, Models and Methods for Functional Data Analysis

功能数据分析的新挑战、模型和方法

• 批准号: RGPIN-2018-06008
• 负责人: Cao, Jiguo
• 金额: $ 2.55万
• 依托单位: Simon Fraser University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2018
• 资助国家: 加拿大
• 起止时间: 2018-01-01 至 2019-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=646808
• 关键词: New; Challenges; Models; Methods; Functional

My research program will develop novel statistical methodologies by addressing applications in various disciplines such as genetics and public health. ******Our first research theme is functional data analysis (FDA), a growing area for analyzing curves, images, or any multidimensional functions. Common sources of functional data include fitness data from wearable devices, air pollution-related data, longitudinal studies, time-course gene expression data, and brain imaging data. The main challenge is dealing with the increasing scale and dimension of functional data while maintaining a balance between the flexibility and interpretability of FDA models. ******We will develop general and efficient FDA methods for high-dimensional functional/scalar variables. This research program will provide the foundation for various large-scale FDA models and have a broad impact in big data analysis. For instance, we will develop air pollution indices for various health outcomes. We will also study the correlation of brain signals among different brain locations. ******Our second research theme focuses on statistical inference for dynamical models. Dynamical models describe the rate of change of a dynamical system by using differential equations (DEs). They are widely used to understand complex systems in areas including biology and physics. While the parameters of DE models usually have scientific interpretations, their values are often unknown and are difficult to estimate. ******We will develop efficient methods that provide accurate and robust parameter estimates for DE models from real data and to link these DE parameters to high-dimensional functional and scalar predictors. This research program will fill the gap between DE modeling and real data analysis and make DE models popular and realistic in practical applications. For example, I propose to model the dynamical mechanism of large-scale networks, which provides not only the connection structure but also the regulation mechanism of networks. The proposed method can be applied to construct time-varying directed neural networks and social networks. I also propose to use partial differential equations to extract information from the seismogram data. This method will use seismogram data to produce high-definition images of subsurface geologic structures. This technology will be extremely useful for Canada's oil industry.******Not only will the proposed research support the training of highly qualified personnel, but it will also result in user-friendly software that we develop as solutions to the research problems tackled. This software will be available to the general public; we anticipate that its use by others will have a broad impact in research and industry. Furthermore, the proposed research is likely to impact the field of statistics through enabling groundbreaking advances in functional data analysis and statistical inference for dynamical models.**************

我的研究计划将通过解决遗传学和公共卫生等各个学科的应用开发新的统计方法。** 我们的第一个研究主题是函数数据分析（FDA），这是一个不断增长的分析曲线，图像或任何多维函数的领域。功能数据的常见来源包括来自可穿戴设备的健身数据、空气污染相关数据、纵向研究、时程基因表达数据和脑成像数据。主要的挑战是处理不断增加的功能数据的规模和维度，同时保持FDA模型的灵活性和可解释性之间的平衡。** 我们将为高维函数/标量变量开发通用和有效的FDA方法。该研究计划将为各种大规模FDA模型提供基础，并在大数据分析中产生广泛影响。例如，我们将为各种健康结果制定空气污染指数。我们还将研究不同大脑位置之间的大脑信号的相关性。** 我们的第二个研究主题是动态模型的统计推断。动力学模型通过使用微分方程（DE）来描述动力学系统的变化率。它们被广泛用于理解生物学和物理学等领域的复杂系统。虽然DE模型的参数通常有科学解释，但它们的值通常是未知的，难以估计。** 我们将开发有效的方法，从真实的数据中为DE模型提供准确和稳健的参数估计，并将这些DE参数与高维函数和标量预测因子联系起来。该研究项目将填补DE建模与真实的数据分析之间的差距，使DE模型在实际应用中更加普及和现实。例如，我建议对大规模网络的动力机制进行建模，它不仅提供了网络的连接结构，而且还提供了网络的调节机制。该方法可用于构造时变有向神经网络和社交网络。我还建议使用偏微分方程来提取地震记录数据的信息。这种方法将利用地震记录数据制作地下地质结构的高清晰度图像。这项技术将对加拿大的石油工业非常有用。拟议的研究不仅将支持高素质人才的培训，而且还将导致我们开发的用户友好的软件，作为解决研究问题的解决方案。该软件将向公众开放;我们预计，其他人使用该软件将对研究和工业产生广泛影响。此外，拟议的研究可能会影响统计领域，通过实现功能数据分析和动态模型统计推断的突破性进展。