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）数据的角度解决了这一挑战。 特别是，重点是对同一对象进行多种类型的测量。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）。 数据分析的挑战是了解不同的测量如何在联合变异模式方面共同工作，以及它们如何在个体变异模式方面独立工作。 提出的新方法被命名为DIVAS，这是“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研究培训机会。DIVAS将在多个方面成为多块数据分析方法的突破。 首先，该算法是完全不同的现有方法，使用一个新的结构，故意设计，以促进部分共享块。 其次，统计推断被有意地纳入DIVAS的各个方面，而不是像大多数竞争方法那样主要是事后的想法。 特别是，我们的应用程序激励推理的分数和负载，这将使用新的主要角度为基础的概念。 第三，该算法是基于扰动界和随机方向界的创新组合，从概率论，线性代数，近似理论和优化的所有思想。 理论验证将使用异常广泛的渐近性进行，这是由驾驶应用的广度所激发的。为确保侧重于方法学最重要的方面，将与其他科学领域的专家（包括未获得资助的合作者）直接合作，开发DIVAS。 一个是乳腺癌研究，它通常涉及非常高维的数据。 我们将在数学上研究具有高维度低样本量渐近性的域，其中对于固定样本量，维度趋于无穷大。 另一个将是果蝇行为遗传学，通常是低维的，这会带来额外的方法学挑战。 在这里，完全不同的经典渐近，其中的样本量增长的固定尺寸，提供了最好的洞察性能的方法。这个奖项反映了NSF的法定使命，并已被认为是值得支持的评估使用基金会的智力价值和更广泛的影响审查标准。

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.