Entropy / CONCEPT
The Feedback Divergence Identity
The average posterior-to-reference divergence of a finite joint law equals its mutual information plus the input-marginal divergence from the reference.
Closed
DIRECT PREREQUISITES1
DIRECT CONSEQUENCES1
PROOF DEPTH3
DOCUMENT LINKS1
Average posterior divergence is mutual information plus input divergence
RELATIONSHIP ATLAS
Every connection, in context.
Direct recorded relationships
Proof dependencyStructural affinityDocument link
Certified topology / UPSTREAM
Prerequisites
Certified topology / DOWNSTREAM
Consequences
RELATED KNOWLEDGE
Structural connections
- Bayes Plausibilitystructural-affinity · Closed
- Counting Hypotheses with Uniform Finite Fanostructural-affinity · Closed
- Estimator-Error Lower Bounds from Finite Fano Inequalitiesstructural-affinity · Closed
- Fano's Method for a Finite Familystructural-affinity · Closed
- Finite Fano with an Arbitrary Observation Referencestructural-affinity · Closed
- Mutual Information as an Entropy Balancestructural-affinity · Closed
- Mutual Information Vanishes on Product Lawsstructural-affinity · Closed
- Nonnegativity of Finite Classical Mutual Informationstructural-affinity · Closed
- Positive Conditioning Preserves Predictive Equivalencestructural-affinity · Closed
- Posterior Mixture Kernel Realizationstructural-affinity · Closed
- Sharp Finite Fano Inequality in Natsstructural-affinity · Closed
- Symmetry of Finite Mutual Informationstructural-affinity · Closed
- Vanishing Mutual Information Characterizes Independencestructural-affinity · Closed
Documents & exposition
Other authored & advisory relationships
None recorded in this release.
LIBRARY / RELEASE VERSIONS
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