Enhanced Statistical Learning for Physical Systems Exploiting Non-Standard Constraints

真实的世界系统通常自然地受到物理定律或人类行为模式的约束，并且通过将所述约束结合到推理机制中可以显著地增强对这样的系统的理解。然而，多个约束的存在会使统计学习的过程复杂化。该项目旨在开发新的统计方法，以帮助解决真实的世界问题，其中大量复杂的约束条件构成推理挑战。动机直接来自三个具体的应用：i）从电形状因子数据中提取质子的半径，这是原子物理学中的一个基本问题，由于来自不同实验模式的结果之间的异常，这是高度相关的，ii）描述风速和从风力涡轮机导出的功率之间的关系，这是发展最快的可再生能源之一，以及iii）用交通速度描述交通流模式，这是交通工程中的关键研究对象。该项目将汇集来自机器学习和贝叶斯非参数化的想法，以开发在约束决策问题中统计上合理和计算上有效的推理方法。该项目旨在开发一种原则性的概率方法，用于科学和工程应用中的推理，其中各种物理约束提供了有关推理关键对象的先验知识。这样的对象可以对应于单个曲线或曲线或密度函数的集合。PI和共同PI将开发新的统计方法，同时纳入多个形状的约束动机的真实的科学和工程应用，而被广泛推广超出所考虑的应用。重点是在一个灵活的非参数贝叶斯模型中获得各种约束的等价表示，并在这些约束空间上开发新的先验分布。贝叶斯方法是有吸引力的，以获得不确定性估计，PI和共同PI的目的是制定严格的理论保证贝叶斯不确定性措施的频率有效性，在目前的设置。此外，PI和co-PI建议证明，包括限制减少了不确定性，这将随后导致更好的科学结论。方法学的发展将伴随着高效的计算算法，以满足特定应用及其他应用所需的可扩展性。为了最大限度地发挥所开发方法的影响，PI和co-PI将与领域专家密切合作，以实现特定的应用。该奖项反映了NSF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。

Real world systems are often naturally constrained by physical laws or human behavioral patterns, and understanding of such systems can be significantly enhanced by incorporating said constraints into the inferential mechanism. However, the presence of multiple constraints can complicate the process of statistical learning. This project aims to develop novel statistical methods to help solve real world problems where a multitude of complex constraints pose inferential challenges. Motivations are drawn directly from three concrete applications: i) extracting the radius of proton from electric form-factor data, a fundamental problem in atomic physics which is of high relevance due to anomalies between results from different modes of experimentation, ii) describing the relationship between wind velocity and power derived from wind-turbines, which is one of the fastest growing renewable sources of energy and iii) describing the traffic flow pattern with traffic speed, a key object of research in traffic engineering. The project will bring together ideas from machine learning and Bayesian nonparametrics to develop statistically sound and computationally efficient methods of inference in constrained decision problems. The project aims to develop a principled probabilistic approach towards inference in scientific and engineering applications where various physical constraints provide a priori knowledge regarding key objects of inference. Such objects may correspond to a single curve or a collection of curves or density functions. The PI and co-PI will develop novel statistical methods for simultaneous incorporation of multiple shape constraints motivated by real scientific and engineering applications, while being broadly generalizable beyond the considered applications. Emphasis is laid on obtaining equivalent representations of various constraints within a flexible nonparametric Bayesian model, and developing novel prior distributions on these constrained spaces. The Bayesian approach is attractive to obtain uncertainty estimates, and the PI and co-PI aim to develop rigorous theoretical guarantees for the frequentist validity of Bayesian uncertainty measures in the present setting. In addition, the PI and co-PI propose to demonstrate that including the constraints diminishes the uncertainty which will subsequently lead to better scientific conclusions. The methodological developments will be accompanied by efficient computation algorithms that meet the scalability demanded by the specific applications and beyond. To maximize the impact of the methodology developed, the PI and co-PI will closely collaborate with domain experts for the specific applications.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.