Distribution of Mutual Information: Difference between revisions

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Created page with "Title: Distribution of Mutual Information Abstract: This research focuses on the distribution of mutual information, a widely used information metric in various fields such as learning Bayesian networks and data analysis. The study aims to derive reliable and computationally efficient analytical expressions for the distribution of mutual information, particularly focusing on the mean, variance, skewness, and kurtosis. The research proposes an exact expression for the me..."
 
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Title: Distribution of Mutual Information
Title: Distribution of Mutual Information


Abstract:
Research Question: How can we determine the distribution of mutual information, a measure of the stochastic dependence between categorical random variables, when considering complete and incomplete data?
This research focuses on the distribution of mutual information, a widely used information metric in various fields such as learning Bayesian networks and data analysis. The study aims to derive reliable and computationally efficient analytical expressions for the distribution of mutual information, particularly focusing on the mean, variance, skewness, and kurtosis. The research proposes an exact expression for the mean and approximate expressions for the variance, which lead to accurate approximations of the distribution of mutual information, even for small sample sizes. The findings of this study have significant implications for the field of information theory and machine learning, as they provide a more accurate and reliable method for estimating the mutual information between two random variables.


Main Research Question:
Methodology: The researchers used a Bayesian framework and a second-order Dirichlet prior distribution to derive the exact analytical expression for the mean, and analytical approximations for the variance, skewness, and kurtosis of mutual information. They considered both complete and incomplete samples, and developed lead ing order approximations for the mean and variance.
How can we derive reliable and computationally efficient analytical expressions for the distribution of mutual information?


Methodology:
Results: The researchers derived analytical expressions for the mean, variance, skewness, and kurtosis of mutual information. They found that these approximations have a guaranteed accuracy level of the order O(n−3), where n is the sample size. They also developed lead ing order approximations for the mean and variance in the case of incomplete samples.
The study utilizes the Bayesian approach, which involves assuming a prior probability density for the unknown parameters. The prior probability density is then used to compute the posterior probability density, from which the distribution of mutual information can be derived. The research focuses on the mean and variance of the distribution, using techniques such as the central limit theorem and the Dirichlet distribution.


Results:
Implications: The derived analytical expressions allow for the distribution of mutual information to be approximated reliably and quickly. This makes mutual information a concrete alternative to descriptive mutual information in many applications that could benefit from moving to the inductive side. The researchers also discussed potential applications, such as feature selection and filter approaches, which could be improved by using inductive mutual information.
The research provides an exact expression for the mean of the distribution of mutual information and approximate expressions for the variance. These expressions lead to accurate approximations of the distribution of mutual information, even for small sample sizes. The study also discusses numerical issues and the range of validity of the proposed method.


Implications:
Link to Article: https://arxiv.org/abs/0403025v1
The findings of this study have significant implications for the field of information theory and machine learning. The proposed method provides a more accurate and reliable method for estimating the mutual information between two random variables, which is crucial for applications such as learning Bayesian networks and data analysis. The research also contributes to the broader field of probability distributions and statistical methods, as it provides new insights into the distribution of mutual information.
 
Link to Article: https://arxiv.org/abs/0112019v1
Authors:  
Authors:  
arXiv ID: 0112019v1
arXiv ID: 0403025v1


[[Category:Computer Science]]
[[Category:Computer Science]]
[[Category:Mutual]]
[[Category:Information]]
[[Category:Information]]
[[Category:Distribution]]
[[Category:Distribution]]
[[Category:Mutual]]
[[Category:Order]]
[[Category:Research]]
[[Category:Analytical]]
[[Category:As]]

Latest revision as of 15:34, 24 December 2023

Title: Distribution of Mutual Information

Research Question: How can we determine the distribution of mutual information, a measure of the stochastic dependence between categorical random variables, when considering complete and incomplete data?

Methodology: The researchers used a Bayesian framework and a second-order Dirichlet prior distribution to derive the exact analytical expression for the mean, and analytical approximations for the variance, skewness, and kurtosis of mutual information. They considered both complete and incomplete samples, and developed lead ing order approximations for the mean and variance.

Results: The researchers derived analytical expressions for the mean, variance, skewness, and kurtosis of mutual information. They found that these approximations have a guaranteed accuracy level of the order O(n−3), where n is the sample size. They also developed lead ing order approximations for the mean and variance in the case of incomplete samples.

Implications: The derived analytical expressions allow for the distribution of mutual information to be approximated reliably and quickly. This makes mutual information a concrete alternative to descriptive mutual information in many applications that could benefit from moving to the inductive side. The researchers also discussed potential applications, such as feature selection and filter approaches, which could be improved by using inductive mutual information.

Link to Article: https://arxiv.org/abs/0403025v1 Authors: arXiv ID: 0403025v1

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