Mutual information is a measure of the amount of information that is shared between two variables. In the case of a Gaussian distribution, it is a measure of the dependence between two Gaussian random variables.
Mutual information from a Gaussian distribution can be calculated using the formula I(X;Y) = 0.5 * log(1 + (r^2 / (1-r^2))), where r is the correlation coefficient between the two variables X and Y.
In a Gaussian distribution, mutual information is directly related to the correlation between two variables. A higher correlation indicates a higher mutual information, while a correlation of 0 indicates no mutual information.
Yes, mutual information can be negative in a Gaussian distribution. This occurs when the correlation between two variables is negative, indicating a negative dependence between the variables.
Mutual information from a Gaussian distribution has many applications in various fields such as signal processing, machine learning, and statistics. It can be used to measure the dependence between variables and to select relevant features for data analysis.