CIF: Small: Learning Low-Dimensional Representations with Heteroscedastic Data Sources

CIF：小：使用异方差数据源学习低维表示

• 批准号: 2331590
• 负责人: Laura Balzano
• 金额: $ 60万
• 依托单位: Regents of the University of Michigan - Ann Arbor
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2024
• 资助国家: 美国
• 起止时间: 2024-01-01 至 2026-12-31
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2331590&HistoricalAwards=false
• 关键词: CIF; Small; Learning; Low; Dimensional

As data-collection efforts continue to grow, so does heterogeneity in data. Machine-learning methods typically assume that data come from a single source or uniform instrumentation with noise characteristics that are the same for every data point. This project will address questions fundamental to learning low-dimensional data representations with heteroscedastic data, wherein samples from different sources have additive noise of different variances. It is well-known that classical linear dimensionality-reduction methods such as principal component analysis (PCA) are sensitive to outliers, so high-variance noise will degrade representations learned by PCA. However, robust methods that simply reject outliers are suboptimal if, indeed, the data do have some signal, even if it is buried in noise. The premise of this project therefore is to use approaches that learn the best way to incorporate the contribution of every different data source, no matter how high- or low-quality, to improve the overall learned representation. Many applications will benefit from the work, including medical imaging, environmental monitoring, astronomical data analysis, computer vision, and bioinformatics. The investigators' prior work in this area indicates that when learning is driven by heterogeneous and heteroscedastic sources – for example, in medical imaging, using data from multiple scanners, or with varying radiation levels – a better model will be learned by actively considering and modeling the heterogeneity. How to optimize learning in the face of such heterogeneity has been so far relatively unstudied, and this research aims to fill that gap. The technical contributions will be in three directions. First, the team of researchers will study open questions regarding how heterogeneity in data affects PCA, including establishing the required sample complexity for learning heteroscedastic models and assessing the optimization landscape of heteroscedastic PCA problems. Second, the team will extend heteroscedastic PCA methods and theory to consider union-of-subspaces models, dictionary learning models, and transform learning models. Third, the investigators will consider how nonlinear low-dimensional embedding methods are affected by heteroscedasticity in the data. The work will focus on distance-based methods and develop a foundational understanding of using distances in machine learning with heterogeneous data sources.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.

随着数据收集工作的不断增长，数据的异质性也随之增长。机器学习方法通​​常假定数据来自单个源或统一仪器，其噪声特性对于每个数据点都相同。该项目将解决使用异性数据学习低维数据表示基础的问题，其中来自不同来源的样本具有不同方差的额外噪声。众所周知，经典的线性维度还原方法（例如主成分分析（PCA））对异常值敏感，因此高变化的噪声将降低PCA学到的表示。但是，如果确实确实有一些信号，那么仅拒绝异常值的强大方法即使在噪声中也有一些信号。因此，该项目的前提是使用方法来学习最佳方法，以纳入每个不同数据源的贡献，无论多么高或低质量，以改善总体学习的代表。许多应用程序将从工作中受益，包括医学成像，环境监测，天文数据分析，计算机视觉和生物信息学。研究人员在该领域的先前工作表明，当学习是由异质和异质源来驱动的，例如，在医学成像中，使用来自多个扫描仪的数据或具有不同辐射水平的数据，将通过积极考虑和建模异质性来学习更好的模型。迄今为止，如何在这种异质性面前优化学习是相对未研究的，这项研究旨在填补这一空白。技术贡献将是三个方向。首先，研究人员团队将研究有关数据中的异质性如何影响PCA的开放问题，包括建立学习异质机模型所需的样本复杂性以及评估异性PCA问题的优化格局。其次，该团队将扩展异质的PCA方法和理论，以考虑掩埋场的模型，字典学习模型和转换学习模型。第三，研究人员将考虑数据中非线性低维嵌入方法如何受到异方差的影响。这项工作将集中在基于距离的方法上，并对使用异质数据来源的机器学习距离进行基本理解。该奖项反映了NSF的法定任务，并通过使用基金会的知识分子优点和更广泛的影响审查标准，通过评估来诚实地支持支持。