CAREER: New Directions for Metric Learning

量化相似性是人工智能和机器学习中的一项基本挑战，如果执行得很完美，许多任务将减少到琐碎的最近邻搜索。例如，确定一封电子邮件是否为垃圾邮件非常简单，只需搜索一个带有标签的电子邮件数据库，并为其分配与被认为最相似的电子邮件相同的标签(垃圾邮件或非垃圾邮件)。但如何衡量两封电子邮件的相似性呢？在比较医学图像时，同样的测量方法仍然适用吗？我们对相似性的理解如何依赖于问题说明？度量学习专门针对给定任务优化距离函数，同时考虑学习问题和数据。线性度量的初步成功表明，许多基于k最近邻的学习任务都有了很大的改善。本项目追求四个研究方向，以加强研究界对度量学习的理论理解，扩大其影响，并显著改善当前的最新水平：1.是否存在导致与现有线性度量一样优雅和有效的优化问题的非线性变换？随着数据集的增长和变得越来越复杂，线性度量不再足以捕获相似关系。通过探索非线性度量的使用，本研究可以大幅提高度量学习的影响和相似关系的准确性。2.度量学习的影响能否扩展到最近邻以外的机器学习框架？设计新的度量学习算法，明确优化各种机器学习算法的距离，将显著增加可以直接受益于度量学习的应用程序和学习方法的数量。3.指标能从弱监管中学习吗？消除对标记数据的依赖将降低度量学习的成本并增加其适用性。4.能否建立一个坚实的理论框架来解释初步的经验成果并指导未来的研究？这将加强研究界对度量学习的理论理解。拟议问题的成功解决将导致新的学习方法，这些方法将立即适用于主要研究人员正在进行的高影响医学研究合作。除了这些研究方向，首席调查员还将追求教育目标，包括共同开发一个K-12课程模块，估计将影响2500名高中生。拟议研究计划中的许多主题都有向本科生和研究生介绍研究过程的理想组成部分，首席研究员计划将他的研究作为指导和激励未来计算机科学家和下一代研究人员的工具。

Quantifying similarity is a fundamental challenge in artificial intelligence and machine learning which - if performed perfectly - would reduce many tasks to a trivial nearest neighbor search. For example, determining whether an email were spam would be as simple as searching a labeled database of emails and assigning it the same label (spam or not) as the email considered most similar to it. But how can one measure the similarity of two email messages? Does the same measurement still apply when comparing medical images? How does our understanding of similarity depend on the problem specification? Metric learning optimizes distance functions specifically for a given task, taking into account both the learning problem and the data. Initial successes with linear metrics show great improvements on many "k-nearest neighbors"-based learning tasks. This project pursues four research directions that strengthen the theoretical understanding of metric learning within the research community, broaden its impact and significantly improve the current state-of-the-art: 1. Are there non-linear transformations that lead to equally elegant and efficient optimization problems as existing linear metrics? As data sets grow and become increasingly complex, linear metrics are no longer sufficient to capture similarity relations. By exploring the use of non-linear metrics, this research can substantially improve the impact of metric learning and the accuracy of similarity relations. 2. Can the impact of metric learning be extended to machine learning frameworks beyond nearest neighbors? Designing new metric learning algorithms that explicitly optimize distances for a broad variety of machine learning algorithms will significantly increase the number of applications and learning methods that can directly benefit from metric learning. 3. Can metrics be learned from weak supervision? Removing the dependency on labeled data will reduce the cost of metric learning and increase its applicability. 4. Can one develop a solid theoretical framework to explain preliminary empirical successes and to direct future research? This will strengthen the theoretical understanding of metric learning within the research community. Successful resolution of the proposed problems will lead to novel learning methods which will be immediately applicable to ongoing high-impact medical research collaborations of the principal investigator. In conjunction with these research directions, the principal investigator will also pursue educational goals, including the co-development of a K-12 curriculum module estimated to impact 2,500 high-school students. Many topics in the proposed research plan have components ideal for introducing the research process to undergraduate and graduate students, and the principal investigator plans to use his research as a vehicle to instruct and inspire future computer scientists and next-generation researchers.