CAREER: Scalable and Robust Uncertainty Quantification using Subsampling Markov Chain Monte Carlo Algorithms

当试图了解复杂系统的工作原理时(无论是单个细胞还是整个生态系统)，大型数据集有可能提供深刻的科学和操作洞察力。然而，有两大挑战必须解决：如何快速而严格地处理如此庞大的数据集，以及如何避免对所得出的结论过于自信，因为数据和对这种系统如何工作的知识的限制。这项研究开发了一套全面的框架和一套算法，以总体上解决这两个挑战，以便科学家和其他数据分析师可以现成地使用它们，从而加快新知识的获得。这项工作将在两个广泛感兴趣的现代应用领域的背景下进行。第一是使生物学家能够了解难以或不可能直接观察到的系统的内部工作原理(如细胞的内部功能或动物物种的进化史)。第二是使生态学家能够预测生态系统在几个月到几十年的时间内如何变化，从而能够更好地管理生态系统和部署生态监测工作。调查员正在与这些应用领域的专家直接合作，以便在这两个领域产生立竿见影的实质性影响。在该项目的一个教育部分，调查员是为波士顿大学本科生开发新的现代应用统计学入门课程团队的核心成员。研究人员还在编写一本关于数据科学算法的设计和分析的易用教科书，这将引起机器学习、数据科学、统计学和相关领域的学生和研究人员的广泛兴趣。尽管取得了许多经验上的成功，但由于缺乏具有严格保证的机器学习方法，导致系统在现实世界中的表现出人意料地糟糕，因此不能被信任用于科学发现和安全关键应用。因此，迫切需要创建可同时扩展到大数据集和机器学习应用程序典型的高维模型的学习算法；能够准确量化不确定性，以确保在模型错误指定、分布偏移和数据损坏的情况下做出正确的决策；并且对于典型的机器学习从业者来说是可靠和易于使用的。该项目的主要技术目标是通过开发具有自动调整程序的可证明正确的次抽样马尔可夫链蒙特卡罗(MCMC)算法，为这些挑战提供全面的解决方案。关键的技术工具是一种统计尺度限制方法，用于建立统计和算法基础，用于如何调整为在潜变量和高斯过程模型中进行推理而设计的基本亚采样MCMC算法，以及用于改进的亚采样MCMC算法，以提高计算效率和数值稳定性。这些理论发展将转化为实用的、用户友好的算法，带有诊断学，告诉用户该理论是否适用于他们的问题。该理论和算法还将扩展到分布稳健损失，如最大平均差异。该研究计划是高度跨学科的，借鉴了大规模概率机器学习、统计学、随机分析、随机过程理论和数值分析的理论和方法。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。

When trying to understand the workings of complex systems (whether it be individual cells or whole ecosystems), large datasets have the potential to provide deep scientific and operational insights. However, there are two major challenges that must be addressed: how to quickly yet rigorously process such large datasets, and how to avoid becoming overconfident in the conclusions reached, given the limitations of the data and knowledge of how such systems work. This research develops a comprehensive framework and set of algorithms for addressing both of these challenges in a general way, so that scientists and other data analysts can use them off-the-shelf, thereby accelerating the acquisition of new knowledge. The work will be developed in the context of two modern application areas of broad interest. The first is to enable biologists to learn about the inner workings of systems that are difficult or impossible to observe directly (such as the internal functioning of cells or the evolutionary history of animal species). The second is to enable ecologists to predict how ecosystems change over periods of time ranging from months to decades, thereby enabling better management of ecosystems and deployment of ecological monitoring efforts. The investigator is working directly with experts in these applications to have an immediate and substantive impact in both areas. In one educational component of the project, the investigator is a core member of the team developing new modern introductory applied statistics courses for undergraduate students at Boston University. The investigator is also writing an accessible textbook on the design and analysis of algorithms for data science, which will be of broad interest to students and researchers in machine learning, data science, statistics, and related fields. Despite many empirical successes, a lack of machine-learning methods with rigorous guarantees has resulted in systems that unpredictably perform poorly in real-world settings and therefore cannot be trusted for scientific discovery and safety-critical applications. Hence, there is an urgent need to create learning algorithms that are simultaneously scalable to the large datasets and high-dimensional models typical of machine-learning applications; able to accurately quantify uncertainty to ensure correct decision-making despite model misspecification, distribution shift, and data corruption; and are reliable and easy-to-use for the typical machine-learning practitioner. The primary technical objective of the project is to provide a comprehensive solution to these challenges by developing provably correct subsampling Markov chain Monte Carlo (MCMC) algorithms with automated tuning procedures. The key technical tool is a statistical-scaling-limits approach to establishing statistical and algorithmic foundations for how to tune basic subsampling MCMC algorithms designed for inference in latent variable and Gaussian process models, and for modified subsampling MCMC algorithms that can improve computational efficiency and numerical stability. These theoretical developments will be translated into practical, user-friendly algorithms with diagnostics that inform the user if the theory is applicable to their problem. The theory and algorithms will also be extended to distributionally robust losses such as maximum mean discrepancy. The research program is highly interdisciplinary, drawing on theory and methods from large-scale probabilistic machine learning, statistics, stochastic analysis, stochastic process theory, and numerical analysis.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.