RI: Small: Collaborative Research: Statistical ranking theory without a canonical loss

对象排序问题在网络搜索和推荐系统等关键技术中占有中心地位。这些技术对数百万人的日常生活产生了巨大的影响。此外，网络上庞大的数据规模使得机器学习在构建排名算法方面特别有吸引力。 大量的研究工作一直致力于开发有效的排名算法，可以处理各种数据集在网络搜索和推荐系统中遇到的。这个项目开发统一的数学理论，将提供一个基础，理解和分类现有的算法，更重要的是，导致更深入的见解和新的算法学习排名的问题。研究人员还将排名算法应用于新领域。 例如，根据化学反应的可分解性对化学反应进行排序，将有助于化学家发现二氧化碳减排和天然气转化为汽油等技术急需的反应基础。排名统计理论的基本进展将纳入本科和研究生课程。所开发的数据集和软件将免费提供给科学界。调查人员还将组织一个研讨会，重点是跨学科的参与和参与的代表性不足的群体在计算机科学和statistics.The主要的技术挑战，在发展统计排名理论是一个普遍认同的损失函数的排名。这与经典的机器学习问题（如分类和回归）形成了鲜明的对比，在经典的机器学习问题中，损失函数只有几种自然的可能性，并且这些可能性在理论上是很好理解的。该项目通过调查不同的排名损失函数如何影响基本的理论属性（如可学习性），并通过创建一个适用于损失函数丰富时的凸代理理论来解决这一差距。 该项目重新审查现有的统计文献排名与计算透镜。 这将有助于开发灵活高效的插件决策规则，对给定输入的标签的条件概率进行建模。通过将这项研究的结果纳入课程和调查文章，PI有助于培养新一代机器学习研究人员和实践者，他们将把排名视为与分类和回归在数学深度和实际重要性方面同等重要的学习问题。 为从业者制定新的排名算法提供理论指导，将改善网络上最常见的应用程序。

The problem of ranking objects occupies a central place in key technologies such as web search and recommendation systems. These technologies have a tremendous daily impact on the lives of millions of people. Moreover, the enormous scale of data on the web makes the use of machine learning especially attractive in constructing ranking algorithms. A huge amount of research effort has been devoted to developing efficient ranking algorithms that can deal with a variety of data sets encountered in web search and recommendation systems.This project develops unifying mathematical theory that will provide a basis for understanding and categorizing existing algorithms and, more importantly, lead to deeper insights and new algorithms for the problem of learning to rank. The investigators also apply ranking algorithms to new domains. For example, ranking chemical reactions based on their plausibility will help chemists discover much-needed reaction bases for technologies such as carbon dioxide reduction, and conversion of natural gas into gasoline. Fundamental advances in the statistical theory of ranking will be incorporated into undergraduate and graduate courses. Data sets and software developed will be made freely available to the scientific community. The investigators will also organize a workshop with a focus on interdisciplinary participation and involvement of under-represented groups in computer science and statistics.The primary technical challenge in developing statistical ranking theory is the absence of a universally agreed-upon loss functions for ranking. This is in contrast to classic machine learning problems such as classification and regression, where there are only a few natural possibilities for the loss function and these are well-understood theoretically. The project addresses this gap by investigating how different loss functions for ranking affect fundamental theoretical properties such as learnability, and by creating a theory of convex surrogates that is applicable when loss functions abound. The project re-examines existing statistical literature on ranking with a computational lens. This will enable development of flexible and efficient plug-in decision rules that model the conditional probability of labels given inputs.By incorporating the results of this research into courses and survey articles, the PIs help train a new generation of machine learning researchers and practitioners who will view ranking as a learning problem on par with classification and regression in mathematical depth as well as practical importance. Theoretical guidance for practitioners formulating new algorithms for ranking will improve the most common applications on the web.