Equitability, Interval Estimation, and Statistical Power

Reshef, Yakir; Reshef, David N.; Sabeti, Pardis C.; Mitzenmacher, Michael

doi:10.1214/19-sts719

Cited by 11 publications

(22 citation statements)

References 41 publications

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“…Equitability is a property of measures of dependence introduced in Reshef et al (2011) and formalized in Reshef et al (2015).…”

Section: A Review Of Equitabilitymentioning

confidence: 99%

“…There are two equivalent ways to view equitability [Reshef et al (2015)]. The first states roughly that an equitable measure of dependence gives similar scores to equally noisy relationships of different types [Reshef et al (2011)].…”

Section: A Review Of Equitabilitymentioning

confidence: 99%

“…Equitability can then be defined via statistical power as follows. DEFINITION 2.1 [Reshef et al (2015)]. Letφ be a statistic, let Q be a set of standard relationships, let : Q → [0, 1], and let 0 < α < 1 − β < 1.…”

Section: A Review Of Equitabilitymentioning

confidence: 99%

“…This is an important goal if there are only a small number of true dependencies in the data, or if our sample size is small enough that only a small number of marginal dependencies can be uncovered. But some high-dimensional data sets contain a very large number of nontrivial relationships, some strong and others weak, and a list of all of them may be too large to allow for detailed model building or for manual followup of each identified relationship [Emilsson et al (2008), Reshef et al (2015)]. For example, in an analysis carried out in Heller et al (2016) of a gene expression data set, five different measures of dependence each identified thousands of relationships-comprising over half of the possible relationships in the data set-as significant after multiple testing correction, and as we show in this paper, a similar phenomenon holds for the aforementioned WHO data set.…”

mentioning

confidence: 99%

“…Equitability, introduced in Reshef et al (2011) and formally defined in Reshef et al (2015), is a property of measures of dependence that addresses this challenge.…”

mentioning

confidence: 99%

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An empirical study of the maximal and total information coefficients and leading measures of dependence

Reshef¹,

Reshef²,

Sabeti³

et al. 2018

Ann. Appl. Stat.

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In exploratory data analysis, we are often interested in identifying promising pairwise associations for further analysis while filtering out weaker 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 and previously formalized, can be used to assess measures of dependence along with the power of their corresponding independence tests and their runtime. Here we present an empirical evaluation of the equitability, power against independence, and runtime of several leading measures of dependence. These include the two recently introduced and simultaneously computable statistics MIC e , whose goal is equitability, and TIC e , whose goal is power against independence. Regarding equitability, our analysis finds that MIC e is the most equitable method on functional relationships in most of the settings we considered. Regarding power against independence, we find that TIC e and Heller and Gorfine's S DDP share state-of-the-art performance, with several other methods achieving excellent power as well. Our analyses also show evidence for a trade-off between power against independence and equitability consistent with recent theoretical work. Our results suggest that a fast and useful strategy for achieving a combination of power against independence and equitability is to filter relationships by TIC e and then to rank the remaining ones using MIC e. We confirm our findings on a set of data collected by the World Health Organization.

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“…Equitability is a property of measures of dependence introduced in Reshef et al (2011) and formalized in Reshef et al (2015).…”

Section: A Review Of Equitabilitymentioning

confidence: 99%

Section: A Review Of Equitabilitymentioning

confidence: 99%

Section: A Review Of Equitabilitymentioning

confidence: 99%

mentioning

confidence: 99%

“…Equitability, introduced in Reshef et al (2011) and formally defined in Reshef et al (2015), is a property of measures of dependence that addresses this challenge.…”

mentioning

confidence: 99%

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