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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：
1912802
负责人：
Nicolas Garcia Trillos
金额：
$ 6.52万
依托单位：
University of Wisconsin-Madison
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 2020-08-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1912802&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，私人投资机构打算揭示看似无关的学习问题和方法之间的隐藏统一，促进理论和计算发展的转移，并统一日益增长的应用文献。这项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例，在考虑不确定性量化的同时获得更准确的预测。PI旨在解决模型的日益复杂和数据集的日益增长给机器学习和逆问题的优化和贝叶斯方法的基础带来的一些新挑战。这个项目将强调统计一致性和算法可伸缩性之间的联系：一致性问题通常在计算上是容易处理的，设计可伸缩算法的一个关键原则是在任何存在的地方利用统计一致性。将进行的具体研究项目有五个主要主题：i)随机数据上定义的离散对象的连续极限的分析。ii)新正则化技术的研究。3)可伸缩采样算法的设计与分析。4)使用复杂模型的离散近似。五)解决方案中的不确定性的量化。要对如此广泛的主题做出实质性的贡献，将需要PIS之间的密切合作。这一奖项反映了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。

项目成果

期刊论文数量（8）

专著数量（0）

科研奖励数量（0）

会议论文数量（0）

专利数量（0）

Geometric structure of graph Laplacian embeddings

DOI：
发表时间：
2019-01
期刊：
J. Mach. Learn. Res.
影响因子：
0
作者：
N. G. Trillos;F. Hoffmann;Bamdad Hosseini
通讯作者：
N. G. Trillos;F. Hoffmann;Bamdad Hosseini

Lipschitz regularity of graph Laplacians on random data clouds

DOI：
10.1137/20m1356610
发表时间：
2020-07
期刊：
ArXiv
影响因子：
0
作者：
J. Calder;N. G. Trillos;M. Lewicka
通讯作者：
J. Calder;N. G. Trillos;M. Lewicka

On the consistency of graph-based Bayesian semi-supervised learning and the scalability of sampling algorithms

基于图的贝叶斯半监督学习的一致性和采样算法的可扩展性

DOI：
发表时间：
2020
期刊：
Journal of machine learning research
影响因子：
6
作者：
Garcia Trillos, Nicolas;Kaplan, Zachary;Samakhoana, Thabo;Sanz-Alonso, Daniel
通讯作者：
Sanz-Alonso, Daniel

From Graph Cuts to Isoperimetric Inequalities: Convergence Rates of Cheeger Cuts on Data Clouds