BIGDATA: F: Big Data Analysis via Non-Standard Property Testing

在当今时代，在广泛的领域中不断产生真正巨大的数据量：这些包括正在进行的大规模科学实验，无处不在的智能手机和传感器，社交媒体上内容的持续生产和演变等等。 如何有效地处理和分析这些海量数据？ 计算机科学的一个分支称为“属性测试”，旨在开发用于分析大量数据集的超快速算法，以快速确定数据是否具有某些感兴趣的属性。 然而，大多数在属性测试中考虑的标准理论模型并不适合许多现实世界的数据分析场景;这些标准模型优先考虑数学优雅，但它们所做的假设与实际数据分析算法的能力或许多实际数据集的性质并不一致。 (As在一个示例中，这些模型通常假设数据分析算法可以合成任意数据点，并查询它们以接收关于这些数据点应该如何被标记的准确信息，但是这样的查询在数据点“原样出现”的许多现实世界设置中是不可能的，并且不能被合成以满足数据分析师的规范。 作为另一个例子，这些模型通常只能处理假设遵循某些高度结构化概率分布的数据，但现实世界的数据是混乱的，很少具有如此高的结构度。 该项目的高级目标是开发和分析属性测试的非标准模型，其明确目标是开发与现实世界数据分析问题的现实和约束相一致的算法。 一个重要的相关目标是促进人力资源开发，方法是对研究生进行外联和培训，包括对历史上代表性不足的群体的成员进行分析和算法技术方面的培训，这对该项目至关重要。 为了实现更广泛的影响，计划开展的活动还包括新课程，调查文章，以及针对小学和中学学生的持续外展活动。更详细地说，该项目将专注于大数据属性测试算法的三个不同方面，所有这些都是出于对真实世界数据分析的考虑：（1）该项目的第一个重点将是开发灵活的算法，用于测试是否已根据“军政府”标记了大量高维数据集-这是一种标记规则，其仅依赖于可能特征的巨大集合中的非常小但未知的数据特征集合。 在他们以前工作的基础上，研究人员将致力于开发军政府测试算法，该算法可以处理任意数据分布和噪声数据，即使只有有限的数据集访问形式也可以成功分析。(2)该项目的第二个重点是将理论机器学习算法的思想和技术转移到海量数据集的属性测试领域。 研究人员以前的工作给出了一个概念验证，说明如何修改（某些相对低效的）机器学习算法，以产生更有效的数据分析属性测试算法，但这种转移只在相对受限的属性测试标准模型中进行，上面提到，假设高度结构化的数据分布。 在这个项目中，研究人员将努力扩展这些早期的结果，以便机器学习技术将产生更灵活的属性测试模型的算法，这些模型具有更大的现实适用性。(3)最后，该项目的第三个重点是开发属性测试算法，这些算法不需要对合成数据点进行查询，而是只使用随机样本，并且可以应用于高维连续数据集。 这种类型的数据通常出现在传感器或不同种类的测量产生数据的设置中，但大多数属性测试算法是为离散二进制值数据而不是连续数据设计的。该奖项反映了NSF的法定使命，并被认为值得通过使用基金会的知识价值和更广泛的影响审查标准进行评估来支持。

In the modern era truly enormous amounts of data are constantly being generated across a wide range of domains: these include ongoing large-scale scientific experiments, ubiquitous smartphones and sensors, the continuous production and evolution of content on social media, and many others. How can this flood of data be efficiently processed and analyzed? A branch of computer science called "property testing" seeks to develop ultra-fast algorithms for analyzing massive data sets to quickly determine whether or not the data has some property of interest. However, the standard theoretical models that have mostly been considered in property testing are not well suited to many real-world data analysis scenarios; these standard models prioritize mathematical elegance, but the resulting assumptions they make do not align well with the abilities of actual data analysis algorithms or with the nature of many actual data sets. (As one example, these models typically assume that a data analysis algorithm can synthesize arbitrary data points and query them to receive accurate information about how such data points should be labeled, but such queries are impossible in many real-world settings where data points "come as they are" and cannot be synthesized to meet the specifications of a data analyst. As another example, these models typically can only deal with data which is assumed to follow certain highly structured probability distributions, but real-world data is messy and rarely possesses such a high degree of structure.) The high-level goal of this project is to develop and analyze non-standard models of property testing, with the explicit goal of developing algorithms which align with the realities and constraints of real-world data analysis problems. An important related goal is to foster human resource development by performing outreach and training graduate students, including members of historically under-represented groups, in the analytic and algorithmic techniques that are central to this project. Planned activities to achieve broader impacts also include new courses, survey articles, and the continuation of outreach activities aimed at students at the elementary and middle school levels.In more detail, the project will focus on three different aspects of property testing algorithms for big data, all of which are motivated by considerations arising from real-world data analysis:(1) The first focus of the project will be on developing flexible algorithms for testing whether a massive high-dimensional data set has been labeled according to a "junta" --- this is a labeling rule which depends only on a very small but unknown set of data features out of a huge set of possible features. Building on their previous work, the investigators will work to develop junta testing algorithms which can handle arbitrary data distributions and noisy data, and can succeed even given only a limited form of access to the data set being analyzed. (2) The second focus of the project will be on transferring ideas and techniques from theoretical machine learning algorithms to the domain of property testing of massive data sets. Previous work of the investigators gave a proof-of-concept for how (certain relatively inefficient) machine learning algorithms can be modified to yield far more efficient property testing algorithms for data analysis, but this transfer went through only in the relatively constrained standard models of property testing, alluded to above, which assume highly structured data distributions. In this project the investigators will work to extend these earlier results so that the machine learning techniques will yield algorithms for more flexible property testing models that are of greater real-world applicability.(3) Finally, the third focus of the project is to develop property testing algorithms which do not need to make queries on synthetic data points but instead use only random samples, and which can be applied to high-dimensional continuous data sets. Data of this type arises commonly in settings where sensors or measurements of different sorts are generating the data, but most property testing algorithms are designed for discrete binary-valued data rather than continuous data.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.