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Divergence

Divergence is a Python package to compute statistical measures of entropy and divergence from probability distributions and samples.

The following functionality is provided:

  • (Information) Entropy [1], [2]
  • Cross Entropy: [3]
  • Relative Entropy or Kullback-Leibler (KL-) Divergence [4], [5]
  • Jensen-Shannon Divergence [6]
  • Joint Entropy [7]
  • Conditional Entropy [8]
  • Mutual Information [9]

The units in which these entropy and divergence measures are calculated can be specified by the user. This is achieved by setting the argument base, to 2.0, 10.0, or np.e.

In a Bayesian context, relative entropy can be used as a measure of the information gained by moving from a prior distribution q to a posterior distribution p.

Installation

    pip install divergence

Examples

See the Jupyter notebook Divergence.

References:

[1] https://en.wikipedia.org/wiki/Entropy_(information_theory)

[2] Shannon, Claude Elwood (July 1948). "A Mathematical Theory of Communication". Bell System Technical Journal. 27 (3): 379–423

[3] https://en.wikipedia.org/wiki/Cross_entropy

[4] https://en.wikipedia.org/wiki/Kullback–Leibler_divergence

[5] Kullback, S.; Leibler, R.A. (1951). "On information and sufficiency". Annals of Mathematical Statistics. 22 (1): 79–86

[6] https://en.wikipedia.org/wiki/Jensen–Shannon_divergence

[7] https://en.wikipedia.org/wiki/Joint_entropy

[8] https://en.wikipedia.org/wiki/Conditional_entropy

[9] https://en.wikipedia.org/wiki/Mutual_information