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

当试图理解复杂系统（无论是单个细胞还是整个生态系统）的工作原理时，大型数据集有可能提供深刻的科学和操作见解。然而，有两个主要的挑战必须解决：如何快速而严格地处理如此大的数据集，以及如何避免对得出的结论过于自信，考虑到数据和系统如何工作的知识的局限性。本研究开发了一个全面的框架和一套算法，以通用的方式解决这两个挑战，以便科学家和其他数据分析人员可以使用现成的框架和算法，从而加速新知识的获取。这项工作将在两个广泛关注的现代应用领域的背景下进行。首先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运作（如细胞的内部功能或动物物种的进化史）。第二个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是如何变化的，从而能够更好地管理生态系统和部署生态监测工作。研究者直接与这些应用领域的专家合作，在这两个领域产生直接和实质性的影响。在该项目的一个教育组成部分中，研究者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的团队的核心成员。研究者还在编写一本关于数据科学算法设计和分析的通俗易懂的教科书，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。尽管在经验上取得了许多成功，但由于缺乏严格保证的机器学习方法，导致系统在现实环境中表现不佳，因此不能被信任用于科学发现和安全关键应用。因此，迫切需要创建能够同时扩展到机器学习应用中典型的大型数据集和高维模型的学习算法；能够准确地量化不确定性，以确保正确的决策，即使模型不规范，分布转移和数据损坏；并且对于典型的机器学习从业者来说是可靠且易于使用的。该项目的主要技术目标是通过开发具有自动调谐程序的可证明正确的子采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。关键技术工具是一种统计尺度限制方法，为如何调整用于潜在变量和高斯过程模型推理的基本子采样MCMC算法以及改进的子采样MCMC算法建立统计和算法基础，从而提高计算效率和数值稳定性。这些理论发展将被转化为实用的、用户友好的算法，并带有诊断，告知用户该理论是否适用于他们的问题。理论和算法也将扩展到分布鲁棒损失，如最大平均差异。该研究项目是高度跨学科的，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。该奖项反映了美国国家科学基金会的法定使命，并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，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.