jhplot.stat

## Class MutualInformation

- java.lang.Object
- jhplot.stat.MutualInformation

public abstract class MutualInformationextends Object

Implements common discrete Mutual Information functions. Provides: Mutual Information I(X;Y), Conditional Mutual Information I(X,Y|Z). Defaults to log_2, and so the entropy is calculated in bits.

### Method Summary

Methods Modifier and Type Method and Description `static double`

**calculateConditionalMutualInformation**(double[] firstVector, double[] secondVector, double[] conditionVector)Calculates the conditional Mutual Information I(X;Y|Z) between two random variables, conditioned on a third.`static double`

**calculateMutualInformation**(double[] firstVector, double[] secondVector)Calculates the Mutual Information I(X;Y) between two random variables.

### Method Detail

#### calculateMutualInformation

public static double calculateMutualInformation(double[] firstVector, double[] secondVector)

Calculates the Mutual Information I(X;Y) between two random variables. Uses histograms to estimate the probability distributions, and thus the information. The mutual information is bounded 0 ≤ I(X;Y) ≤ min(H(X),H(Y)). It is also symmetric, so I(X;Y) = I(Y;X).- Parameters:
`firstVector`

- Input vector (X). It is discretised to the floor of each value before calculation.`secondVector`

- Input vector (Y). It is discretised to the floor of each value before calculation.- Returns:
- The Mutual Information I(X;Y).

#### calculateConditionalMutualInformation

public static double calculateConditionalMutualInformation(double[] firstVector, double[] secondVector, double[] conditionVector)

Calculates the conditional Mutual Information I(X;Y|Z) between two random variables, conditioned on a third. Uses histograms to estimate the probability distributions, and thus the information. The conditional mutual information is bounded 0 ≤ I(X;Y) ≤ min(H(X|Z),H(Y|Z)). It is also symmetric, so I(X;Y|Z) = I(Y;X|Z).- Parameters:
`firstVector`

- Input vector (X). It is discretised to the floor of each value before calculation.`secondVector`

- Input vector (Y). It is discretised to the floor of each value before calculation.`conditionVector`

- Input vector (Z). It is discretised to the floor of each value before calculation.- Returns:
- The conditional Mutual Information I(X;Y|Z).

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