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的最新进展至关重要。它们已经被用于计算机科学的几乎每个领域以及自然科学、工程和社会科学的许多领域。机器学习的中心任务是“训练”模型，这需要在一组训练示例中寻找最小化某些性能指标的模型。这样的性能指标被称为总损失，它与在单个训练示例上测量模型质量的个体损失不同。聚合损失作为连接训练数据和待学习模型的纽带，是机器学习算法中的一个基本组成部分，其理论和实际意义值得进行全面系统的研究。拟议的工作将集中在几个基本的研究问题有关的总损失：是否有任何其他类型的总损失以外的平均个人损失？如果是，这些新的总损失的一般抽象公式是什么？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重点。第一个推力探索了二进制分类的基于秩的聚合损失的新类型，并研究了优化基于它们形成的学习目标的有效算法。新的总损失将被应用到问题，如对象检测，其中基于排名的评估指标是占主导地位。第二个推力旨在加深我们对使用基于秩的总损失开发的二进制分类算法的理解，并将重点研究其统计理论，如泛化和一致性。第三个重点是将新类型的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）和无监督学习。第四个推力致力于理论方面的综合损失，其中一个综合损失将抽象为一组函数，映射到一个数字的个人损失的合奏。这个抽象将被利用来研究新的总损失的属性，使他们比平均损失上级，并提出新的总损失超越排名为基础的。这个奖项反映了NSF的法定使命，并已被认为是值得通过使用基金会的智力价值和更广泛的影响审查标准进行评估的支持。

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.