AF: Small: The Geometry of Learning on Structured Data Objects

AF：小：结构化数据对象学习的几何

• 批准号: 2115677
• 负责人: Jeff Phillips
• 金额: $ 49.94万
• 依托单位: University of Utah
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2021
• 资助国家: 美国
• 起止时间: 2021-10-01 至 2024-09-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2115677&HistoricalAwards=false
• 关键词: AF; Small; Geometry; Learning; Structured

The project builds connections between computational geometry and machine learning by extending and demonstrating how advances in geometry can impact and inform machine learning, and vice versa. Computational geometry offers many ways to characterize and compute on shapes in low dimensions (such as spatially-encoded trajectories of people or objects) and provides understanding about point sets in high dimensions. Machine learning focuses on automatically discovering patterns which generalize across a population to new data. This project will leverage computational geometry insights to make analysis of low-dimensional shapes more amenable to machine learning, and to improve understanding and efficacy of high-dimensional data analysis. The project will also help bridge these connections by supporting several events including international workshops on geometry in machine learning, and community building ones in data science. In more detail, this project highlights two keystone applications. The first is dealing with trajectories, which can be modeled as time-parameterized curves in a spatial domain and pose many challenges for direct use within typical analysis pipelines. The developed approach shows how to convert such objects (and related low-dimensional geometric structures) into a vectorized representation so it can seamlessly integrate with numerous data-analysis tasks. The second is in analyzing data sets already embedded as points in a high-dimensional space. Word vector representations are a central and important such example where the individual data-point coordinates do not have meaning. Hence, the project uses the geometry of these high-dimensional data sets to provide richer analytical operations and more intuitive and transparent 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.

该项目通过扩展和展示几何进步如何影响和指导机器学习，建立计算几何和机器学习之间的联系，反之亦然。 计算几何提供了多种方法来表征和计算低维度的形状（例如人或物体的空间编码轨迹），并提供对高维度点集的理解。 机器学习专注于自动发现可在人群中泛化为新数据的模式。 该项目将利用计算几何见解，使低维形状的分析更适合机器学习，并提高对高维数据分析的理解和效率。 该项目还将通过支持多项活动来帮助弥合这些联系，包括机器学习中的几何国际研讨会和数据科学中的社区建设研讨会。 更详细地说，该项目重点介绍了两个关键应用程序。 第一个是处理轨迹，它可以建模为空间域中的时间参数化曲线，并且对在典型分析流程中直接使用提出了许多挑战。 开发的方法展示了如何将此类对象（以及相关的低维几何结构）转换为矢量化表示，以便它可以与众多数据分析任务无缝集成。 第二个是分析已经作为点嵌入高维空间中的数据集。 词向量表示是一个核心且重要的示例，其中各个数据点坐标没有意义。 因此，该项目利用这些高维数据集的几何形状来提供更丰富的分析操作和更直观、透明的分析。该奖项反映了 NSF 的法定使命，并通过使用基金会的智力价值和更广泛的影响审查进行评估，认为值得支持标准。

项目成果

VERB: Visualizing and Interpreting Bias Mitigation Techniques Geometrically for Word Representations

• DOI: 10.1145/3604433
• 发表时间: 2023-06
• 期刊: ACM Transactions on Interactive Intelligent Systems
• 影响因子: 3.4
• 作者: Archit Rathore;Yan Zheng;Chin-Chia Michael Yeh

Interpretable Debiasing of Vectorized Language Representations with Iterative Orthogonalization

通过迭代正交化矢量化语言表示的可解释去偏

• 发表时间: 2023
• 期刊: International Conference on Learning Representations
• 作者: Prince Osei Aboagye;Yan Zheng;Jack Shunn;Chin-Chia Michael Yeh;Junpeng Wang;Zhongfang Zhuang;Huiyuan Chen;Liang Wang;Wei Zhang;Jeff Phillips
• 通讯作者: Jeff Phillips

An experimental study on classifying spatial trajectories

• DOI: 10.1007/s10115-022-01802-5
• 发表时间: 2022-12
• 期刊: Knowledge and Information Systems
• 影响因子: 2.7
• 作者: H. Pourmahmood-Aghababa;J. M. Phillips

Normalization of Language Embeddings for Cross-Lingual Alignment

• 发表时间: 2022
• 期刊: ArXiv
• 作者: P. Aboagye;Yan Zheng;Chin-Chia Michael Yeh;Junpeng Wang;Wei Zhang;Liang Wang;Hao Yang;J. M. Phillips

Using Existential Theory of the Reals to Bound VC Dimension

• 发表时间: 2022
• 作者: Austin Watkins