RI: Small: A Study of New Aggregate Losses for Machine Learning

机器学习对人工智能和大数据分析领域的最新进展起到了重要作用。它们已经被用于计算机科学的几乎所有领域以及自然科学、工程和社会科学的许多领域。机器学习的中心任务是“训练”一个模型，这需要在一组训练示例中寻找最小化某些性能度量的模型。这种性能指标被称为总损失，它将与衡量单个训练样本模型质量的单个损失区分开来。作为连接训练数据和待学习模型的纽带，总损失是机器学习算法中的一个基本组成部分，其理论和实践意义值得全面系统地研究。建议的工作将集中在与总损失有关的几个基本研究问题上：除了平均个人损失之外，是否还有其他类型的总损失？如果有，这些新的总损失的一般抽象公式将是什么？新的总损失如何适应不同的机器学习问题？以及使用一般总损失的机器学习算法的统计和计算行为是什么？该项目的技术目标分为四个相互关联的目标。第一个主旨是探索基于排名的二值分类总损失的新类型，并研究在此基础上形成的优化学习目标的高效算法。新的总损失将应用于目标检测等问题，其中主要使用基于排名的评估度量。第二个重点是加深我们对使用基于排名的总损失的二进制分类算法的理解，并将重点研究它们的统计理论，如泛化和一致性。第三个重点将把对新型总损失的研究扩展到其他监督问题(多类和多标签学习和监督度量学习)和非监督学习。第四个重点致力于总损失的理论方面，其中总损失将被抽象为一个集合函数，将单个损失的集合映射到一个数字。这一抽象将被用于研究新的总损失的属性，使其优于平均损失，并在基于排名的损失之外提出新的总损失。该奖项反映了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。

Machine learning is instrumental for the recent advances in AI and big data analysis. They have been used in almost every area of computer science and many fields of natural sciences, engineering, and social sciences. The central task of machine learning is to “train” a model, which entails seeking models that minimize certain performance metrics over a set of training examples. Such performance metrics are termed as the aggregate losses, which are to be distinguished from the individual losses that measures the quality of the model on a single training example. As the link between the training data and the model to be learned, the aggregate loss is a fundamental component in machine learning algorithms, and its theoretical and practical significance warrants a comprehensive and systematic study. The proposed work will focus on several fundamental research questions concerning the aggregate loss: are there any other types of aggregate loss beyond the average individual losses?; if so, what will be a general abstract formulation of these new aggregate loss?; how can the new aggregate losses be adapted to different machine learning problems?; and what are the statistical and computational behaviors of machine learning algorithms using the general aggregate losses?. The technical aims of the project are divided into four interrelated thrusts. The first thrust explores new types of rank-based aggregate losses for binary classification and study efficient algorithms optimizing learning objectives formed based upon them. The new aggregate losses will be applied to problems such as object detection, where rank-based evaluation metric is used dominantly. The second thrust aims to deepen our understanding of the binary classification algorithms developed using the rank-based aggregate losses and will be focused on a study of their statistical theories such as generalization and consistency. The third thrust will extend the study of new types of aggregate losses to other supervised problems (multi-class and multi-label learning and supervised metric learning) and unsupervised learning. The fourth thrust dedicates to the theoretical aspects of aggregate losses, in which an aggregate loss will be abstracted as a set function that maps the ensemble of individual losses to a number. This abstraction will be exploited to study the properties of new aggregate losses that make them superior than the average loss and propose new aggregate losses beyond rank-based ones.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.