排序偏好数据的双样本检验及建模假设的作用
Two-Sample Testing on Ranked Preference Data and the Role of Modeling Assumptions
摘要：
许多应用程序需要对排名偏好数据进行双样本测试。例如，在众包中，人们提供的成对比较数据是否与评级转换为比较的数据类似，这是一个长期存在的问题。其他例子包括体育数据分析和同行评分。本文针对两两比较数据和排序数据设计了两样本检验。对于成对比较数据的双样本检验，我们建立了正确区分两组样本分布所需的样本复杂度的上限。我们的测试基本上不需要对分布做任何假设。然后，我们证明互补的下界表明，我们的结果是紧（在极大极小意义上）的常数因子。我们通过证明一系列成对比较模型（WST，MST，SST，基于参数的BTL和Thurstone）的下限来研究建模假设的作用。我们还提供了测试算法和相关的样本复杂性界限的问题，两个样本测试的部分（或全部）rankingdata.Therefore，我们经验性地评估我们的结果，通过广泛的模拟，以及两个现实世界的数据集组成的成对比较。通过将我们的双样本测试应用于现实世界的成对比较数据，我们得出结论，人们提供的评级和排名确实分布不同。另一方面，我们的测试承认欧洲足球队在两个赛季的相对表现没有显着差异。最后，我们将我们的双样本测试应用于真实世界的部分和总排名数据集，并发现基于性别，年龄和居住地区的人口统计学划分中的寿司偏好存在统计学显著差异。
英文摘要：
A number of applications require two-sample testing on ranked preference data. For instance, in crowdsourcing, there is a long-standing question of whether pairwise comparison data provided by people is distributed similar to ratings-converted-to-comparisons. Other examples include sports data analysis and peer grading. In this paper, we design two-sample tests for pairwise comparison data and ranking data. For our two-sample test for pairwise comparison data, we establish an upper bound on the sample complexity required to correctly distinguish between the distributions of the two sets of samples. Our test requires essentially no assumptions on the distributions. We then prove complementary lower bounds showing that our results are tight (in the minimax sense) up to constant factors. We investigate the role of modeling assumptions by proving lower bounds for a range of pairwise comparison models (WST, MST,SST, parameter-based such as BTL and Thurstone). We also provide testing algorithms and associated sample complexity bounds for the problem of two-sample testing with partial (or total) ranking data.Furthermore, we empirically evaluate our results via extensive simulations as well as two real-world datasets consisting of pairwise comparisons. By applying our two-sample test on real-world pairwise comparison data, we conclude that ratings and rankings provided by people are indeed distributed differently. On the other hand, our test recognizes no significant difference in the relative performance of European football teams across two seasons. Finally, we apply our two-sample test on a real-world partial and total ranking dataset and find a statistically significant difference in Sushi preferences across demographic divisions based on gender, age and region of residence.
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。
