Residual Entropy

The residual entropy, or erasure entropy, is a dual to the binding information.

\[\begin{split}\R[X_{0:n}] &= \sum \H[X_i | X_{\{0..n\}/i}] \\ &= - \sum_{x_{0:n} \in X_{0:n}} p(x_{0:n}) \log_2 \prod p(x_i|x_{\{0:n\}/i})\end{split}\]
The residual entropy :math:`\R[X:Y]` The residual entropy :math:`\R[X:Y:Z]`
residual_entropy(dist, rvs=None, crvs=None, rv_names=None)[source]
Parameters :
  • dist (Distribution) – The distribution from which the residual entropy is calculated.
  • rvs (list, None) – The indexes of the random variable used to calculate the residual entropy. If None, then the total correlation is calculated over all random variables.
  • crvs (list, None) – The indexes of the random variables to condition on. If None, then no variables are condition on.
  • rv_names (bool) – If True, then the elements of rvs are treated as random variable names. If False, then the elements of rvs are treated as random variable indexes. If None, then the value True is used if the distribution has specified names for its random variables.
Returns:

R (float) – The residual entropy

Raises :

ditException – Raised if dist is not a joint distribution.

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