Data Integration Via Analysis of Subspaces (DIVAS)

分析大数据的一个挑战是经常同时生成的多种测量类型。本研究从多块(也称为多视图)数据的角度来解决这一挑战。特别是，重点是对相同对象进行的多种类型的测量。一个常见的例子是生物学和医学中的多个“组学”测量(例如，基因和蛋白质表达)。数据分析的挑战是理解不同的测量如何在联合变化模式方面共同工作，以及它们如何在单独的变化模式方面独立工作。拟议的新方法被命名为DIVAS，是通过子空间分析进行数据集成的首字母缩写。一个重要的基本主题是，最有用的新数据分析方法是在跨学科合作的背景下发明的。该项目还为研究生提供了研究培训机会。DiVAS将在几个方面突破多块数据的分析方法。首先，该算法与现有方法完全不同，使用了一种专门为促进部分共享块而设计的新结构。其次，统计推断被刻意融入到DIVA的各个方面，而不是像大多数竞争方法那样主要是事后考虑。特别是，我们的应用程序激发了对分数和负载的推理，这将使用基于新的主要角度的概念来执行。第三，该算法基于摄动界和随机方向界的创新组合，吸取了概率论、线性代数、逼近理论和最优化的全部思想。理论验证将使用异常广泛的渐近性，这是由驾驶应用的广度所驱动的。为确保将重点放在方法的最重要方面，将与其他科学领域的专家(包括无资金支持的合作者)直接合作开发DIVAS。其中一项是乳腺癌研究，通常涉及非常高维的数据。我们将用数学方法研究这个领域，它具有高维、低样本量的渐近性，其中对于固定样本量，维度趋于无穷大。另一门是典型低维的果蝇行为遗传学，这带来了额外的方法论挑战。在这里，完全不同的经典渐近性，其中样本大小为固定维度增长，提供了对方法性能的最佳洞察。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

A challenge In analyzing big data is that of multiple measurement types that are often generated simultaneously. This research addresses this challenge from the perspective of multi-block (also known as multi-view) data. In particular, the focus is on multiple types of measurements made on the same objects. One common example is that of multiple 'omics' measurements (e.g. gene and protein expression) in biology and medicine. The data analytic challenge is to understand how the different measurements work together, in terms of modes of joint variation, and how they work independently in terms of individual modes of variation. The proposed new methodology is named DIVAS, an acronym for Data Integration Via Analysis of Subspaces. An important underlying theme is that the most useful new data analytic methods are invented in the context of interdisciplinary collaboration. The project also provides research training opportunities for graduate students. DIVAS will be a breakthrough in analysis methods for multi-block data in several ways. First, the algorithm is completely different from existing methods, using a new structure deliberately designed to facilitate partially shared blocks. Second, statistical inference is deliberately incorporated into all aspects of DIVAS, instead of being mostly an after-thought as in most competing methods. In particular, our applications motivate inference on both scores and loadings, which will be performed using novel principal angle based concepts. Third, the algorithm is based on an innovative combination of perturbation bounds and random direction bounds which draws on ideas from all of probability theory, linear algebra, approximation theory and optimization. Theoretical validation will be performed using an unusually broad range of asymptotics, that is motivated by the breadth of the driving applications. To ensure focusing on the most important aspect of the methodology, development of DIVAS will be done in direct collaboration with experts (including unfunded collaborators) in other scientific areas. One will be breast cancer research, which typically involves very high dimensional data. We will mathematically investigate that domain with High Dimension Low Sample Size asymptotics, where the dimensions go to infinity for fixed sample size. The other will be Drosophila behavioral genetics with typically low dimension, which creates additional methodological challenges. Here the completely different classical asymptotics, where the sample size grows for fixed dimension, provide the best insights into performance of the method.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.