不完全排序统计分析的多分辨率分析框架
A Multiresolution Analysis Framework for the Statistical Analysis of Incomplete Rankings
摘要：
虽然排名数据的统计分析在过去几个世纪一直是人们感兴趣的主题，特别是在经济学，心理学或社会选择理论中，但在过去的15年中，它已经被最近的应用程序（如推荐或搜索引擎）重新激活，并且现在在机器学习文献中受到越来越多的关注。许多现代系统确实生成排名数据，例如表示查询的有序结果或用户偏好。每个这样的排名通常只涉及整个项目目录的一个小的但变化的子集。然而，这些数据的变异性研究，即不完全排序的统计分析，是一个巨大的统计和计算挑战，因为它们的异质性和相关的组合问题的复杂性。虽然许多用于分析完整排名（目录中所有项目的排序）的统计方法都记录在专门的文献中，部分排名（带领带的完整排名）或成对比较，但今天只有少数方法可用于处理不完整的排名，每种方法都依赖于强有力的特定假设。这篇文章的目的是介绍一个新的一般框架的统计分析不完全排名。它是基于一个专门为这些特定的数据，其建设也解释了这里，这符合自然的多尺度结构的不完整的排名，并提供了一个新的分解的排名信息与多分辨率分析解释（MRA）的表示。我们表明，MRA表示自然允许克服统计和计算的挑战，而无需对数据进行任何结构性假设。因此，它提供了一个通用和灵活的框架，以解决各种各样的统计问题，其中数据的形式是不完整的排名。
英文摘要：
Though the statistical analysis of ranking data has been a subject of interest over the past centuries, especially in economics, psychology or social choice theory, it has been revitalized in the past 15 years by recent applications such as recommender or search engines and is receiving now increasing interest in the machine learning literature. Numerous modern systems indeed generate ranking data, representing for instance ordered results to a query or user preferences. Each such ranking usually involves a small but varying subset of the whole catalog of items only. The study of the variability of these data, i.e. the statistical analysis of incomplete rank-ings, is however a great statistical and computational challenge, because of their heterogeneity and the related combinatorial complexity of the problem. Whereas many statistical methods for analyzing full rankings (orderings of all the items in the catalog) are documented in the dedicated literature, partial rankings (full rankings with ties) or pairwise comparisons, only a few approaches are available today to deal with incomplete ranking, relying each on a strong specific assumption. It is the purpose of this article to introduce a novel general framework for the statistical analysis of incomplete rankings. It is based on a representation tailored to these specific data, whose construction is also explained here, which fits with the natural multi-scale structure of incomplete rankings and provides a new decomposition of rank information with a multiresolu-tion analysis interpretation (MRA). We show that the MRA representation naturally allows to overcome both the statistical and computational challenges without any structural assumption on the data. It therefore provides a general and flexible framework to solve a wide variety of statistical problems, where data are of the form of incomplete rankings.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
