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Selecting Multiple Biomarker Subsets with Similarly Effective Binary Classification Performances

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Bounds on mutual information of mixture data for classification tasks.

Yijun Ding, Amit Ashok

Journal of the Optical Society of America. A, Optics, Image Science, and Vision

|October 10, 2022

Summary

This study introduces new methods to calculate Shannon mutual information for mixture data, crucial for classification tasks in imaging. These techniques offer efficient ways to estimate performance when analytical solutions are unavailable.

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Area of Science:

Information Theory
Machine Learning
Image Analysis

Background:

Shannon mutual information is a key metric for classification performance, linked to error probability.
Imaging data often follows mixture distributions, posing challenges for mutual information calculation.
Existing methods lack analytical or efficient computational solutions for mixture data.

Purpose of the Study:

To develop novel bounds and approximations for mutual information in mixture models.
To enable accurate performance quantification for classification tasks with complex data.
To address the computational limitations of current information-theoretic metrics.

Main Methods:

Introduced a variational upper bound and a lower bound for mutual information.
Developed three novel approximations utilizing pair-wise divergences between mixture components.
Compared proposed methods against Monte Carlo sampling and entropy-based bounds.

Main Results:

The proposed bounds and approximations provide viable alternatives for estimating mutual information.
Numerical simulations demonstrate the effectiveness and efficiency of the new methods.
Performance evaluation confirms the utility of the developed techniques in practical scenarios.

Conclusions:

The introduced information-theoretic tools effectively quantify classification performance for mixture data.
These methods overcome limitations of analytical and computational approaches.
The study advances the application of information theory in machine learning and image analysis.