[论文解读] An Empirical Study of Leading Measures of Dependence

David N. Reshef, Yakir Reshef+2 more|arXiv (Cornell University)|May 9, 2015

Mental Health Research Topics参考文献 21被引用 10

一句话总结

该论文对MICe和TICe——两种专为高维数据探索设计的现代相关性度量方法——进行了实证评估，重点考察其公平性、对独立性的统计功效以及计算效率。MICe在按R²公平排名噪声功能性关系方面表现优异，而TICe则在对独立性的统计功效方面达到最先进水平；作者建议采用TICe进行预过滤，随后再计算MICe，以在关联检测中实现敏感性与公平性的最佳平衡。

ABSTRACT

In exploratory data analysis, we are often interested in identifying promising pairwise associations for further analysis while filtering out weaker, less interesting ones. This can be accomplished by computing a measure of dependence on all variable pairs and examining the highest-scoring pairs, provided the measure of dependence used assigns similar scores to equally noisy relationships of different types. This property, called equitability, is formalized in Reshef et al. [2015b]. In addition to equitability, measures of dependence can also be assessed by the power of their corresponding independence tests as well as their runtime. Here we present extensive empirical evaluation of the equitability, power against independence, and runtime of several leading measures of dependence. These include two statistics introduced in Reshef et al. [2015a]: MICe, which has equitability as its primary goal, and TICe, which has power against independence as its goal. Regarding equitability, our analysis finds that MICe is the most equitable method on functional relationships in most of the settings we considered, although mutual information estimation proves the most equitable at large sample sizes in some specific settings. Regarding power against independence, we find that TICe, along with Heller and Gorfine's S^DDP, is the state of the art on the relationships we tested. Our analyses also show a trade-off between power against independence and equitability consistent with the theory in Reshef et al. [2015b]. In terms of runtime, MICe and TICe are significantly faster than many other measures of dependence tested, and computing either one makes computing the other trivial. This suggests that a fast and useful strategy for achieving a combination of power against independence and equitability may be to filter relationships by TICe and then to examine the MICe of only the significant ones.

研究动机与目标

• 评估主流依赖度量方法（包括MICe和TICe）的公平性、统计功效及计算效率。
• 确定MICe和TICe是否在不同函数形式与噪声水平下，对关系强度的排序表现更优。
• 评估理论研究中提出的公平性与对独立性的统计功效之间的权衡关系是否在实践中可测量。
• 为探索性数据分析中在MICe、TICe及其他依赖度量方法之间的选择，提供实用且基于数据的指导。

提出的方法

• 研究在广泛的数据生成模型、关系类型及样本量下进行了大量实证评估。
• 公平性通过比较噪声功能性关系的得分与其潜在R²值来衡量，MICe与互信息估计作为主要基准。
• 对独立性的统计功效通过Simon和Tibshirani（2012）提供的关系集合进行评估，比较各度量方法的检验表现。
• 计算效率通过测量在多种样本量和变量维度下的运行时间来评估。
• MICe与TICe同步计算，利用其计算关联性，实现高效的两阶段过滤。
• 各度量方法的参数设置在每次分析中均经过优化，以确保比较的公平性与现实性。

实验结果

研究问题

• RQ1 在不同样本量和关系类型下，MICe相较于其他度量方法，在按R²公平排名噪声功能性关系方面表现如何？
• RQ2 MICe、TICe及其他依赖度量方法在独立性检验中，对广泛备择假设的相对统计功效如何？
• RQ3 如理论所预测，实践中是否存在可测量的公平性与对独立性统计功效之间的权衡？
• RQ4 TICe能否作为有效预过滤步骤，在应用MICe前减少候选关系数量，同时不丢失重要关联？
• RQ5 与其它主流依赖度量方法相比，MICe与TICe在计算效率方面表现如何？

主要发现

• 在大多数测试设置中，MICe是对功能性关系最公平的方法，尽管在特定情况下，互信息估计在大样本量时表现更优。
• TICe与Heller和Gorfine的SDDP在所测试的关系中均实现了对独立性的最先进统计功效。
• 实证结果明确证实了公平性与对独立性统计功效之间的权衡，与Reshef等人[2015b]的理论预期一致。
• MICe与TICe显著快于其他多数依赖度量方法，且TICe可实现高效的关系预过滤。
• 计算TICe可轻松获得MICe的值，表明存在一种实用的两阶段工作流：先用TICe过滤，再仅对显著结果计算MICe。
• 结果表明，由于TICe具备高统计功效与计算效率，特别在与MICe结合使用时，是更优的预过滤统计量。