Modelling modern data objects: statistical methods for high-dimensionality and intricate correlation structures

现代数据对象建模：高维和复杂相关结构的统计方法

• 批准号: RGPIN-2020-06941
• 负责人: FerreiraMiranda, Michelle
• 金额: $ 1.31万
• 依托单位: University of Victoria
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2022
• 资助国家: 加拿大
• 起止时间: 2022-01-01 至 2023-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=758963
• 关键词: Modelling; modern; data; objects; statistical

Advances in technology have been generating data with increased complexity. Modern data objects are often high-dimensional and can lay in 2D, 3D and even 4D Euclidean and non-Euclidean spaces. Examples of such functions can arise in a wide range of scenarios, such as wearable devices, imaging recordings, medical imaging studies, eye-tracking devices, custom made instruments, and others. It is usually of interest to associate these complex functions to other covariates of interest, often scalars, which is the main focus of this proposal. In the literature, these models are known as function-on-scalar regression models (functional response regression models) or scalar-on-function regression models (predictive models). Most of the methodological contributions in functional regression models were initially developed for the first generation functional data which consists of simple smooth functions, typically one dimensional. We build up on previous ideas of data decorrelation and dimensionality reduction to bring a new set of tools that are able to handle the intricate correlation structures inherent in more complex functional data, while simultaneously addressing data high-dimensionality. We handle the complex correlation structures by devising an adaptive basis strategy that provides the foundation for borrowing information within functions. We also propose to develop a criteria to perform basis selection that automatically reduces data dimensionality. The methodology will be embedded in a Bayesian framework with shrinkage priors, that allows us to obtain MCMC samples in the basis space that are easily converted into MCMC samples in the data space through the use of basis inverse transforms. We will also develop an algorithm that will scale up to large datasets and a software package that will be easily accessible and open source. The proposed program is suitable for all HQP expertise level and facilitate their learning of skills in a way that is appropriate for both academia and industry. The contributions that will result from this program will definitely have an impact in advancing the statistical methods to include the latest data advancement.

技术的进步一直在生成复杂性增加的数据。现代数据对象通常是高维的，可以放在2D，3D甚至4D欧几里得和非欧几里得空间中。此类功能的示例可能会在各种场景中出现，例如可穿戴设备，成像录制，医学成像研究，远射设备，定制仪器等。通常，将这些复杂功能与其他感兴趣的协变量相关联，通常是标量，这是该提案的主要重点。在文献中，这些模型被称为功能 - 刻录回归模型（功能响应回归模型）或标量 - 功能回归模型（预测模型）。功能回归模型中的大多数方法论贡献最初是针对第一代功能数据开发的，该功能数据由简单的平滑函数组成，通常是一个维度。 我们建立了以前的数据去相关性和降低性降低的想法，以携带一组能够处理更复杂功能数据中固有的复杂的相关结构的新工具，同时解决数据高差异性。我们通过设计一种自适应基础策略来处理复杂的相关结构，该策略为在功能中借用信息奠定了基础。我们还建议制定一个标准，以执行自动降低数据维度的基础选择。该方法将嵌入带有收缩先验的贝叶斯框架中，这使我们能够在基本空间中获取MCMC样品，这些框架可以通过使用基础逆变换来轻松地将其转换为数据空间中的MCMC样品。我们还将开发一种算法，该算法将扩展到大型数据集和一个容易访问和开源的软件包。拟议的计划适合所有HQP专业知识水平，并以适合学术界和行业的方式促进他们的技能学习。该计划将造成的贡献肯定会影响统计方法以包括最新数据进步。