Methodologies for Modeling and Analyzing Massive Environmental and Biomedical Data Sets

大量环境和生物医学数据集的建模和分析方法

• 批准号: RGPIN-2014-05193
• 负责人: Provost, Serge
• 金额: $ 0.8万
• 依托单位: University of Western Ontario
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2015
• 资助国家: 加拿大
• 起止时间: 2015-01-01 至 2016-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=588265
• 关键词: Methodologies; Modeling; Analyzing; Massive; Environmental

Nowadays, high throughput data arising for instance in biostatistics-especially those observed in connection with gene expression studies-and in the environmental sciences-for instance, meteorological data transmitted from satellites-must be rapidly analyzed. Innovative techniques such as those based on samples moments, which the applicant has previously advocated, or those relying on the Bayesian approach, which are discussed in several of his papers, shall be further developed and adapted to data mine such massive sets of observations. Since complex data frequently involve several variables, I also plan to extend the semi-parametric univariate moment-based density estimation techniques that I have introduced to the multivariate context. Novel multivariate data visualization techniques that would be suited to certain types of large data sets shall be proposed as well. Extant distributional results on singular quadratic forms in Gaussian and elliptically contoured vectors shall be extended to the Hermitian case and to generalized quadratic expressions, which involve random matrices in lieu of random vectors. The bivariate density estimation techniques introduced by the applicant at the last annual meeting of The International Environmentrics Society, which consists in expressing joint density estimates in terms the product of the density estimates of the marginal distributions and a polynomial adjustment whose coefficients are determined from a moment matching technique, will be extended to multivariate settings. Once evaluated at the inverse distribution functions of the marginals, such a polynomial turns out to be a copula density. This approach arguably gives rise to the most flexible type of copulae one could devise. This methodology shall be applied to colossal data sets arising from various fields of scientific investigation such as environmetrics, financial modeling, econometrics and genomic studies. Being merely based on a finite number of joint sample moments, such techniques should prove more suitable than, for instance, kernel density estimates for modeling series of observations that can be construed as "big data", as they readily produce density estimates in a functional form that lends itself to algebraic manipulations. Given their computational simplicity, moment-based data mining methods ought to efficiently assist researchers in detecting anomalies, patterns and dependencies in large and complex data sets. I also intend to develop software documentation and source code to facilitate the implementation of the aforementioned distributional methodologies. Additionally, monographs on the evaluation of the distribution of various types of quadratic forms and on moment-based density estimation and approximation techniques are planned.

如今，必须快速分析生物统计学等领域（尤其是与基因表达研究相关的观察到的数据）和环境科学（例如卫星传输的气象数据）中产生的高通量数据。创新技术，例如申请人之前提倡的基于样本矩的技术，或在他的几篇论文中讨论的依赖贝叶斯方法的技术，应进一步开发并适应对如此大量的观察数据进行数据挖掘。由于复杂数据经常涉及多个变量，因此我还计划将我引入的半参数单变量基于矩的密度估计技术扩展到多变量环境中。还应提出适合某些类型的大型数据集的新颖的多变量数据可视化技术。高斯和椭圆轮廓向量中奇异二次形式的现有分布结果应扩展到埃尔米特情况和广义二次表达式，其中涉及随机矩阵代替随机向量。申请人在国际环境学会上届年会上提出的双变量密度估计技术，包括用边际分布的密度估计和多项式调整的乘积来表达联合密度估计，多项式调整的系数是从时刻确定的匹配技术将扩展到多变量设置。一旦在边缘的逆分布函数上进行评估，这样的多项式就会成为一个联结密度。这种方法可以说产生了人们可以设计的最灵活的系词类型。该方法应适用于环境计量学、金融建模、计量经济学和基因组研究等科学研究各个领域产生的庞大数据集。由于仅基于有限数量的联合样本矩，此类技术应该比核密度估计更适合用于建模可被解释为“大数据”的一系列观测值，因为它们很容易在函数中产生密度估计。适合代数运算的形式。鉴于其计算简单性，基于矩的数据挖掘方法应该能够有效地帮助研究人员检测大型复杂数据集中的异常、模式和依赖性。我还打算开发软件文档和源代码，以促进上述分布式方法的实施。此外，还计划出版有关评估各种类型的二次形式分布以及基于矩的密度估计和近似技术的专着。