Entropy / CONCEPT
Markov Data Processing
For a finite Markov chain X to Y to Z, observing the channel output Z cannot reveal more about X than observing the intermediate variable Y.
Closed
DIRECT PREREQUISITES1
DIRECT CONSEQUENCES9
PROOF DEPTH6
DOCUMENT LINKS1
Zero conditional mutual information is conditional factorization
RELATIONSHIP ATLAS
Every connection, in context.
Direct recorded relationships
Proof dependencyStructural affinityDocument link
Certified topology / UPSTREAM
Prerequisites
Certified topology / DOWNSTREAM
Consequences
- Canonical Predictive-State Sufficiencytruth-dependency · Closed
- Coarse-Graining Cannot Add Informationtruth-dependency · Closed
- Conditional Information and Support Sufficiencytruth-dependency · Closed
- Entropy of a Commonly Determined Statetruth-dependency · Closed
- Fano Error Bounds after Finite Channelstruth-dependency · Closed
- Mutual-Information Chain Ruletruth-dependency · Closed
- Positive-Prior Conditional Independencetruth-dependency · Closed
- Prediction Closure Criteriontruth-dependency · Closed
- Translation Loss under Postprocessingtruth-dependency · Closed
RELATED KNOWLEDGE
Structural connections
- Author Information Decompositionstructural-affinity · Closed
- Canonical Conditional Information Submodularitystructural-affinity · Closed
- Canonical Predictive-State Sufficiencystructural-affinity · Closed
- Classical Markov monogamy for every permutationstructural-affinity · Closed
- Coarse-Graining Cannot Add Informationstructural-affinity · Closed
- Conditional Choice-Outcome Chain Rulestructural-affinity · Closed
- Conditional Information and Support Sufficiencystructural-affinity · Closed
- Conditional Mutual Informationstructural-affinity · Closed
- Conditional-Independent Information Submodularitystructural-affinity · Closed
- Entropy of a Commonly Determined Statestructural-affinity · Closed
- Fano Error Bounds after Finite Channelsstructural-affinity · Closed
- Macroscopic Predictive Efficiency Increasestructural-affinity · Closed
- Mutual-Information Chain Rulestructural-affinity · Closed
- Positive-Prior Conditional Independencestructural-affinity · Closed
- Prediction Closure Criterionstructural-affinity · Closed
- Strong Subadditivity and Conditional Productsstructural-affinity · Closed
- Translation Loss under Postprocessingstructural-affinity · Closed
- Vanishing Mutual Information Characterizes Independencestructural-affinity · Closed
Documents & exposition
Other authored & advisory relationships
None recorded in this release.
LIBRARY / RELEASE VERSIONS
Content history
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