Distribution of Mutual Information

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 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: How can we derive reliable and computationally efficient analytical expressions for the distribution of mutual information?

Methodology: 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: 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: 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: arXiv ID: 0112019v1