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 CONSEQUENCES8
PROOF DEPTH6
DOCUMENT LINKS1
The mutual-information gap is a conditional-information gap
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
- 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
- Coarse-Graining Cannot Add Informationstructural-affinity · Closed
- Conditional Choice-Outcome Chain Rulestructural-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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