Entropy / CONCEPT
Conditional Entropy and Its Chain Rule
Finite conditional entropy in nats is the marginal-weighted entropy of conditional slices and satisfies the entropy chain rule.
Closed
DIRECT PREREQUISITES2
DIRECT CONSEQUENCES7
PROOF DEPTH3
DOCUMENT LINKS1
Joint entropy obeys the chain rule
RELATIONSHIP ATLAS
Every connection, in context.
Direct recorded relationships
Proof dependencyStructural affinityDocument link
Certified topology / UPSTREAM
Prerequisites
Certified topology / DOWNSTREAM
Consequences
- Conditioning Reduces Entropytruth-dependency · Closed
- Entropy and Capacity under Carrier Forgettingtruth-dependency · Closed
- Expected Posterior Entropy Reductiontruth-dependency · Closed
- Future-Word Information Chaintruth-dependency · Closed
- Nonnegativity of Finite Entropytruth-dependency · Closed
- Strong Subadditivity and Conditional Productstruth-dependency · Closed
- Weak Finite Fano Inequality in Natstruth-dependency · Closed
RELATED KNOWLEDGE
Structural connections
- Bayes Plausibilitystructural-affinity · Closed
- Chain Rule for Finite Classical KL Divergencestructural-affinity · Closed
- Collision Entropy versus Shannon Entropystructural-affinity · Closed
- Collision-Entropy Uncertaintystructural-affinity · Closed
- Conditioning Reduces Entropystructural-affinity · Closed
- Coordinate Necessity of the Adjudication Signaturestructural-affinity · Closed
- Entropy and Capacity under Carrier Forgettingstructural-affinity · Closed
- Expected Posterior Entropy Reductionstructural-affinity · Closed
- Future-Word Information Chainstructural-affinity · Closed
- Marginal Monotonicity of Finite Classical KL Divergencestructural-affinity · Closed
- Maximum Entropy on a Finite Alphabetstructural-affinity · Closed
- Mutual Information Vanishes on Product Lawsstructural-affinity · Closed
- Nonnegativity of Finite Entropystructural-affinity · Closed
- Positive Conditioning Preserves Predictive Equivalencestructural-affinity · Closed
- Posterior Mixture Kernel Realizationstructural-affinity · Closed
- Strong Subadditivity and Conditional Productsstructural-affinity · Closed
- The Entropy-Divergence Consistency Identitystructural-affinity · Closed
- The X-state conditional entropy f_1 need not be weakly unimodalstructural-affinity · Closed
- Weak Finite Fano Inequality in Natsstructural-affinity · Closed
Documents & exposition
Other authored & advisory relationships
None recorded in this release.
LIBRARY / RELEASE VERSIONS
Content history
Loading release versions...
Browse the archiveCertified provenance