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Discovering General Multidimensional Associations.

Ben Murrell1, Daniel Murrell2, Hugh Murrell3

  • 1Department of Medicine, University of California San Diego, San Diego, United States of America.

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|March 19, 2016
PubMed
Summary
This summary is machine-generated.

We developed a new method to estimate explained variance (R2) for unknown relationships, outperforming existing measures like Maximal Information Coefficient (MIC). This approach works in multiple dimensions and controls for covariates, offering a robust way to measure variable association.

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Area of Science:

  • Statistics
  • Data Science
  • Machine Learning

Background:

  • The coefficient of determination (R2) quantifies variance explained by a function for known relationships.
  • Estimating explained variance equitably for unknown or non-linear relationships remains a challenge.
  • Existing methods like Maximal Information Coefficient (MIC) have limitations in power and convergence.

Purpose of the Study:

  • To develop a generalized R2 estimation method for unknown functional relationships.
  • To compare the performance of the new method against MIC.
  • To extend the method for multivariate relationships and covariate control.

Main Methods:

  • Direct estimation of a generalized R2 for unknown relationships.
  • Performance evaluation against the Maximal Information Coefficient (MIC).
  • Extension to higher dimensions and conditional association analysis.

Main Results:

  • The proposed method provides equitable estimation of explained variance.
  • It demonstrates higher statistical power than MIC for detecting associations.
  • Faster convergence with increasing sample size was observed.
  • The approach successfully generalizes to multivariate and conditional association analyses.

Conclusions:

  • A novel, equitable, and powerful method for estimating generalized R2 is presented.
  • This method offers advantages over MIC, particularly for complex relationships.
  • The approach is versatile, applicable to multivariate and conditional analyses, with an available R package (matie).