# Measuring Dependence Powerfully and Equitably

@article{Reshef2016MeasuringDP, title={Measuring Dependence Powerfully and Equitably}, author={Yakir A Reshef and David N. Reshef and Hilary K. Finucane and Pardis C Sabeti and Michael Mitzenmacher}, journal={ArXiv}, year={2016}, volume={abs/1505.02213} }

Given a high-dimensional data set we often wish to find the strongest relationships within it. A common strategy is to evaluate a measure of dependence on every variable pair and retain the highest-scoring pairs for follow-up. This strategy works well if the statistic used is equitable [Reshef et al. 2015a], i.e., if, for some measure of noise, it assigns similar scores to equally noisy relationships regardless of relationship type (e.g., linear, exponential, periodic).
In this paper, we…

## 58 Citations

### Equitability, interval estimation, and statistical power

- MathematicsArXiv
- 2015

This work formally present and characterize equitability, a property of measures of dependence that enables fruitful analysis of data sets with a small number of strong, interesting relationships and a large number of weaker ones, and draws on the equivalence of interval estimation and hypothesis testing to draw on this property.

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

- Computer Science
- 2018

An empirical evaluation of the equitability, power against independence, and runtime of several leading measures of dependence, including the two recently introduced and simultaneously computable statistics MIC e and TIC e, whose goal is equitability.

### An Empirical Study of Leading Measures of Dependence

- Computer ScienceArXiv
- 2015

An extensive empirical evaluation of the equitability, power against independence, and runtime of several leading measures of dependence finds that MICe is the most equitable method on functional relationships in most of the settings the authors considered, although mutual information estimation proves themost equitable at large sample sizes in some specific settings.

### Theoretical Foundations of Equitability and the Maximal Information Coefficient

- Computer ScienceArXiv
- 2014

This paper formalizes the theory behind both equitability and MIC in the language of estimation theory and proves an alternate, equivalent characterization of MIC that is used to state new estimators of it as well as an algorithm for explicitly computing it when the joint probability density function of a pair of random variables is known.

### A Robust-Equitable Measure for Feature Ranking and Selection

- Computer ScienceJ. Mach. Learn. Res.
- 2017

A new concept of robust-Equitability is introduced and a robust-equitable copula dependence measure is identified, the robustCopula dependence (RCD) measure, which is based on the L1-distance of the copula density from uniform and it is proved theoretically that RCD is much easier to estimate than mutual information.

### Symmetric rank covariances: a generalized framework for nonparametric measures of dependence

- Mathematics, Computer ScienceBiometrika
- 2018

Symmetric Rank Covariances is a new class of multivariate nonparametric measures of dependence that generalises all of the above measures and leads naturally to multivariate extensions of the Bergsma--Dassios sign covariance.

### The randomized information coefficient: assessing dependencies in noisy data

- Computer ScienceMachine Learning
- 2017

This work formally establishes the importance of achieving low variance when comparing relationships using the mutual information estimated with grids and experimentally demonstrates the effectiveness of RIC for detecting noisy dependencies and ranking dependencies for the applications of genetic network inference and feature selection for regression.

### Design and adjustment of dependency measures

- Computer Science
- 2015

This thesis formalizes a framework to adjust dependency measures in order to correct for biases and applies adjustments to existing dependency measures between variables and shows how to achieve better interpretability in quantification.

### Estimating scale-invariant directed dependence of bivariate distributions

- MathematicsComput. Stat. Data Anal.
- 2021

### A Copula Statistic for Measuring Nonlinear Multivariate Dependence

- Computer Science
- 2016

A new index based on empirical copulas, termed the Copula Statistic (CoS), is introduced for assessing the strength of multivariate dependence and for testing statistical independence. New properties…

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This work formally present and characterize equitability, a property of measures of dependence that enables fruitful analysis of data sets with a small number of strong, interesting relationships and a large number of weaker ones, and draws on the equivalence of interval estimation and hypothesis testing to draw on this property.

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- Computer ScienceArXiv
- 2015

An extensive empirical evaluation of the equitability, power against independence, and runtime of several leading measures of dependence finds that MICe is the most equitable method on functional relationships in most of the settings the authors considered, although mutual information estimation proves themost equitable at large sample sizes in some specific settings.

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