BIGDATA: F: Scalable Bayes Uncertainty Quantification with Guarantees

数据数量和种类的增加带来了机遇，但其中许多数据没有得到仔细管理，导致了不确定性。 需要数据分析技术来准确地描述不确定性。 该项目开发了管理不确定性的原则性方法，特别是通过聚类和子集数据，然后结合子集分析的结果。 将数据划分为更小的问题可以保证大数据的可扩展性，而联合收割机的能力以理论上合理的方式管理大数据集合中固有的不确定性。关键思想是子集后验的Wasserstein重心可以用于有效地执行后验近似。 该项目扩展了对Wasserstein重心的理论理解，增强了建模不确定性的能力。 新的数学工具正在开发中，以限制问题的大小和性质以及计算时间方面的近似精度。 这些算法在各种各样的海量数据集上进行评估，从大规模网络到收集大量生物标志物的生物医学数据集。 此外，该项目还为大数据分析领域的年轻人才提供跨学科培训，以提高劳动力的竞争力，并增加数据科学研究人员的队伍。

Increasing volume and variety of data opens opportunities, but much of these data are not carefully curated, leading to uncertainty. Data analysis techniques are needed that accurately characterize uncertainty. This project develops principled approaches to managing uncertainty, particularly through clustering and subsetting data, and then combining results from analysis of the subsets. Dividing data into smaller problems promises scalability to Big Data, while the ability to combine results in a theoretically sound manner manages the uncertainty inherent in large data collections.The key idea is that Wasserstein barycenter of subset posteriors can be used to efficiently perform posterior approximation. The project extends the theoretical understanding of Wasserstein barycenters, enhancing ability to model uncertainty. New mathematical tools are being developed to bound the accuracy of approximations in terms of the problem's size and nature, and computational time. The algorithms are evaluated on a rich variety of massive data sets, ranging from large-scale networks to biomedical data sets collecting huge numbers of biomarkers. In addition, the project provides interdisciplinary training to young talent in big data analytics to improve competitiveness of the workforce and increase the cohort of data science researchers.