Difference between revisions of "Entropy, Relative Entropy, Mutual Information"
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The entropy of a discrete random variable is | The entropy of a discrete random variable is | ||
| − | <math>H\left(X\right)=-\sum_{x} p\left(x\right) \log_2\left(p\left(x\right)\right)</math> | + | {{NumBlk|:|<math>H\left(X\right)=-\sum_{x\in \mathcal{X}} p\left(x\right) \log_2\left(p\left(x\right)\right)</math>|{{EquationRef|1}}}} |
Revision as of 13:28, 25 June 2020
Definitions
Entropy
- a measure of the uncertainty of a random variable
- The entropy of a random variable is a measure of the uncertainty of the random variable
- it is a measure of the amount of information required on the average to describe the random variable
Relative Entropy
- a measure of the distance between two distributions
- a measure of the inefficiency of assuming that the distribution is when the true distribution is .
Mutual Information
- a measure of the amount of information that one random variable contains about another random variable
Entropy
The entropy of a discrete random variable is
-
(1)
