Collaborative Research: Machine Learning and Inverse Problems in Discrete and Continuous Settings

协作研究：离散和连续环境中的机器学习和反问题

基本信息

批准号：
1912818
负责人：
Daniel Sanz-Alonso
金额：
$ 5.86万
依托单位：
University of Chicago
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2019
资助国家：
美国
起止时间：
2019-06-15 至 2021-05-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1912818&HistoricalAwards=false
关键词：
Collaborative Research Machine Learning Inverse

项目摘要

The goal of this project is to push forward the principled use of data in science and applications. By means of rigorous mathematical analysis, the PIs intend to uncover the hidden unity of seemingly unrelated learning problems and methodologies, facilitating the transfer of theoretical and computational developments and unifying the growing applied literature. The proposed work intends to partially satisfy the societal and scientific need to build paradigms that combine data and complex mathematical models to obtain more accurate predictions while accounting for uncertainty quantification.The PIs intend to address some of the new challenges that the increasing complexity of models and the growing size of data sets have brought to the foundations of optimization and Bayesian approaches to machine learning and inverse problems. This project will emphasize the connection between statistical consistency and algorithmic scalability: consistent problems are often computationally tractable, and a key principle for the design of scalable algorithms is to exploit statistical consistency wherever present. The specific research projects that will be pursued have five overarching themes: i) The analysis of continuum limits of discrete objects defined on random data.ii) The study of new regularization techniques. iii) The design and analysis of scalable sampling algorithms. iv) The use of discrete approximations of complex models. v) The quantification of uncertainty in the solutions. Contributing in a substantial manner to this wide range of themes will require close collaboration between the PIs.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.

该项目的目标是推动数据在科学和应用中的原则性使用。通过严格的数学分析，PI 旨在揭示看似无关的学习问题和方法论的隐藏统一性，促进理论和计算发展的转移，并统一不断增长的应用文献。拟议的工作旨在部分满足社会和科学的需求，即建立结合数据和复杂数学模型的范式，以获得更准确的预测，同时考虑不确定性量化。 PI 旨在解决模型复杂性不断增加和数据集规模的不断增长为机器学习和逆问题的优化和贝叶斯方法奠定了基础。该项目将强调统计一致性和算法可扩展性之间的联系：一致问题通常在计算上是可以处理的，可扩展算法设计的一个关键原则是利用存在的统计一致性。将进行的具体研究项目有五个总体主题：i）对随机数据定义的离散对象的连续极限进行分析。ii）新的正则化技术的研究。 iii）可扩展采样算法的设计和分析。 iv) 使用复杂模型的离散近似。 v) 解决方案中不确定性的量化。对如此广泛的主题做出实质性贡献需要 PI 之间的密切合作。该奖项反映了 NSF 的法定使命，并且通过使用基金会的智力价值和更广泛的影响审查标准进行评估，被认为值得支持。