jensen_shannon_divergence

infomeasure.jensen_shannon_divergence(*data, approach: str | None = None, **kwargs)

Calculate the Jensen-Shannon Divergence between two or more distributions.

The Jensen-Shannon Divergence is a symmetrized and smoothed version of the Kullback-Leibler Divergence. It is calculated as the average of the Kullback-Leibler Divergence between each distribution and the average distribution.

\[JSD(P \| Q) = \frac{1}{2} KL(P \| M) + \frac{1}{2} KL(Q \| M)\]

where \(M = \frac{1}{2} (P + Q)\).

Parameters:

parray_like

The first data.

qarray_like

The second data.

…array_like

Further data to compare.

approachstr

The name of the entropy estimator to use.

**kwargsdict

Additional keyword arguments to pass to the entropy estimator.

Returns:

float

The Jensen-Shannon Divergence.

Raises:

ValueError

If the approach is not supported or the entropy estimator is not compatible with the Jensen-Shannon Divergence.

ValueError

If any of the given data is not an array-like object.