BIGDATA: F: Scalable Bayes Uncertainty Quantification with Guarantees

不断增加的数据量和种类带来了机会，但这些数据中的许多没有经过仔细的管理，导致了不确定性。需要准确描述不确定性的数据分析技术。这个项目开发了管理不确定性的原则性方法，特别是通过对数据进行分类和子集划分，然后结合子集分析的结果。将数据分成更小的问题保证了大数据的可扩展性，而以理论上合理的方式组合结果的能力管理了大型数据收集所固有的不确定性。其关键思想是子集后验的Wasserstein重心可以有效地执行后验逼近。该项目扩展了对沃瑟斯坦重心的理论理解，增强了对不确定性进行建模的能力。正在开发新的数学工具，根据问题的大小和性质以及计算时间来限制近似的精度。这些算法在各种海量数据集上进行了评估，从大规模网络到收集大量生物标记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，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.