Point Impact and Sparsity in Functional Data Analysis.

函数数据分析中的点影响和稀疏性。

• 批准号: 8505504
• 负责人: IAN WRAY MCKEAGUE
• 金额: $ 17.43万
• 依托单位: COLUMBIA UNIVERSITY HEALTH SCIENCES
• 依托单位国家: 美国
• 财政年份: 2011
• 资助国家: 美国
• 起止时间: 2011-09-01 至 2015-06-30
• 项目状态: 已结题
• 来源: https://reporter.nih.gov/project-details/8505504
• 关键词: Accounting; Address; Adult; Affect; Base Pairing; Behavior; Cancer Patient; Characteristics; Chromosomes; Clinical; Collaborations; Collection; Complex; DNA Methylation; Data; Data Analyses; Data Set; Development; Diagnosis; Disease Outcome; Doctor of Philosophy; Epidemiology; Equation; Famines; Fractals; Gene Expression; Gene Expression Profile; Genes; Genetic; Genomics; Goals; Growth; Intake; Joints; Learning; Life Cycle Stages; Linear Regressions; Literature; Machine Learning; Mammary Neoplasms; Measurement; Methodology; Methods; Modeling; Molecular Profiling; Outcome; Perinatal; Positioning Attribute; Procedures; Prognostic Marker; Property; Public Health; Public Health Applications Research; Resolution; Staging; Statistical Methods; Students; System; Testing; Time; Work; base; cardiovascular risk factor; data modeling; epidemiology study; estrophilin; flexibility; genome-wide; improved; indexing; insight; interest; malignant breast neoplasm; neuropsychological; novel; response; theories; tumor

DESCRIPTION (provided by applicant): This is a project to develop new methods of functional data analysis directed towards important public health applications in genomics and life course epidemiology. In genome-wide expression and DNA methylation studies, it is of interest to locate genes showing activity that is associated with clinical outcomes, e.g., to use gene expression profiles from the tumors of breast cancer patients to predict estrogen receptor protein concentration, an important prognostic marker for breast tumors. In such studies, the gene expression profile across a chromosome can be regarded a functional predictor, and a gene associated with the clinical outcome is identified by its base pair position along the chromosome. The key aim of the project is to develop new methods of statisti- cal inference for finding such genetic loci, leading to the identification of chromosomal regions that are potentially useful for diagnosis and therapy. Although there is extensive statistical literature on gene expression data, it is almost exclusively concerned with multiple testing procedures for detecting the presence of differentially expressed genes, and statistical methods for locating such genes based on expression profiles (interpreted as functional predictors) are not well developed. Although functional data analysis has reached a mature stage of development over the last ten years, serious problems can arise when the currently available methods are applied in situations involving functional predictors (or trajectories) that have point impact effects (as with gene expression), or in situations in which there is only sparse temporal resolution in the observation of the trajectories. The broad objectives of the project are to exploit fractal behavior in the trajectories to improve statistical learning methodology in functional data analysis. The project will have important implications for understanding a wide variety of complex adaptive systems having fractal behavior. Studies of calorie-intake trajectories and DNA methylation profiles related to cardiovascular risk outcomes, and growth rate trajectories related to neuropsychological outcomes, will be developed as applications of the new methodology. The first specific problem to be addressed is to show that the rates of learning in systems involving trajectories with fractal characteristics are determined by the Hurst parameter (i.e., the exponent of self-similarity scaling) and to show that a type of bootstrap learning can adapt to the full range of fractal behavior. The second specific problem to be addressed is to develop an imputation method for generating missing values of trajectories that have fractal properties (e.g., growth rate curves), and to find a way to carry out functional regression modeling based on the imputed trajectories. 1

描述（由申请人提供）：这是一个项目，旨在开发针对基因组学和生命课程的重要公共卫生应用的新方法分析。在全基因组表达和DNA甲基化研究中，找到与临床结果相关的活性的基因，例如，使用乳腺癌患者肿瘤的基因表达谱以预测雌激素受体蛋白浓度，这是乳腺癌的重要预后标记。在此类研究中，可以认为跨染色体的基因表达谱是一个功能预测因子，并且与临床结果相关的基因通过其沿染色体的基对位置确定。该项目的主要目的是开发用于寻找这种遗传基因座的统计学推断的新方法，从而鉴定出潜在的诊断和治疗有用的染色体区域。尽管有关基因表达数据的广泛统计文献，但它几乎完全关注用于检测差异表达基因的多个测试程序，并且基于表达谱（解释为功能预测指标）定位此类基因的统计方法并未得到很好的发展。尽管在过去的十年中，功能数据分析已经达到了成熟的发展阶段，但是当在涉及功能性预测因子（或轨迹）的情况下使用当前可用的方法（与基因表达一样），或者在观察轨迹的观察中只有稀疏的时间分辨率分辨率时，就会出现严重问题。该项目的广泛目标是利用轨迹中的分形行为，以改善功能数据分析中的统计学习方法。该项目将对理解具有分形行为的各种复杂自适应系统具有重要意义。对与心血管风险结果相关的卡路里 - 智能轨迹和DNA甲基化谱的研究以及与神经心理结局相关的增长率轨迹将被开发为新方法的应用。要解决的第一个具体问题是表明，涉及具有分形特征的轨迹的系统中的学习速率取决于Hurst参数（即自相似性缩放的指数），并表明一种自举学习可以适应整个分形行为。要解决的第二个特定问题是开发一种插补方法来生成具有分形特性（例如增长率曲线）的轨迹的缺失值，并找到一种基于估算轨迹的功能回归建模的方法。 1