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Related Experiment Video

Updated: Jun 3, 2026

Quantification of Information Encoded by Gene Expression Levels During Lifespan Modulation Under Broad-range Dietary Restriction in C. elegans

Quantification of Information Encoded by Gene Expression Levels During Lifespan Modulation Under Broad-range Dietary Restriction in C. elegans

Published on: August 16, 2017

Lower bounds on mutual information.

David V Foster¹, Peter Grassberger

¹Complexity Science Group, University of Calgary, Calgary, Canada.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|March 17, 2011

Summary

This summary is machine-generated.

This study corrects previous claims on mutual information bounds. We demonstrate that bounds using linear correlations depend on variable distributions, offering new insights with gene expression data.

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Area of Science:

Information Theory
Statistical Analysis
Bioinformatics

Background:

Mutual Information (MI) quantifies statistical dependence between random variables.
Previous work established lower bounds on MI for real-valued variables.
These bounds are crucial for understanding complex systems and data analysis.

Purpose of the Study:

To correct and refine existing lower bounds on mutual information (MI).
To investigate the dependence of these bounds on marginal distributions of variables.
To explore practical applications of these refined bounds, particularly in biological data.

Main Methods:

Theoretical analysis of mutual information and correlation measures.
Derivation of bounds based on marginal distributions (Gaussian and uniform).
Application of rank-based transformations to enforce uniform marginals and use Spearman correlations.
Analysis of gene expression datasets to validate the bounds.

Main Results:

Demonstrated that non-trivial lower bounds on MI depend on marginal distributions.
Identified Gaussian and uniform distributions as yielding simplest and most practical bounds, respectively.
Showcased the utility of Spearman correlation coefficients for bounding MI via rank transformation.
Revealed nontrivial bounds in gene expression data, with saturation degree offering valuable insights.

Conclusions:

Existing claims regarding mutual information lower bounds require correction due to distribution dependence.
Rank-based transformations provide a robust method for establishing practical MI bounds.
The derived bounds offer significant utility for analyzing complex datasets, such as gene expression data.