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，高通量的数据，例如在生物农药，特别是那些观察到的基因表达研究，并在环境科学，例如，从卫星传输的气象数据，必须迅速分析。创新技术，如申请人以前提倡的基于样本矩的技术，或申请人在几篇论文中讨论的依赖贝叶斯方法的技术，应进一步发展和调整，以挖掘如此大量的观测数据。由于复杂的数据经常涉及多个变量，我还计划将我介绍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。新的多元数据可视化技术，将适合于某些类型的大型数据集，以及提出。关于高斯和椭圆轮廓向量中奇异二次型的现有分布结果应推广到厄米特情形和广义二次表达式，其中涉及随机矩阵代替随机向量。由申请人在国际环境学会的最后一次年度会议上介绍的双变量密度估计技术，其中包括在表示联合密度估计的边际分布和多项式调整，其系数是从一个时刻匹配技术确定的产品，将被扩展到多变量设置。一旦在边缘的逆分布函数处求值，这样的多项式就变成了copula密度。可以说，这种方法产生了人们所能设计的最灵活的连接类型。这种方法应适用于从各种科学调查领域产生的庞大数据集，如计量经济学，金融建模，计量经济学和基因组研究。仅仅基于有限数量的联合样本矩，这样的技术应该证明比例如核密度估计更适合于对可以被解释为“大数据”的一系列观测进行建模，因为它们容易以函数形式产生密度估计，该函数形式适合于代数操作。由于其计算简单，基于矩的数据挖掘方法应该有效地帮助研究人员在大型和复杂的数据集检测异常，模式和依赖关系。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，还计划编写关于评价各种二次型的分布以及关于基于矩的密度估计和近似技术的专著。