trureturingGitHub MATHEMATICAL ATLAS

Divergence / CONCEPT

Classical Data Processing as a Chain Identity

The finite classical data-processing identity from two decompositions of joint relative entropy.

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THEOREM

Joint relative entropy has two chain decompositions

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Classical Data Processing as a Chain IdentityClassical Data Processing as aChain IdentityChain Rule for Finite Classical KL DivergenceChain Rule for Finite ClassicalKL DivergenceNonnegativity of the Classical Data-Processing DefectNonnegativity of the ClassicalData-Processing DefectEquality in Gibbs' InequalityEquality in Gibbs' InequalityThe Grandmother TheoremThe Grandmother TheoremThe Classical Petz Equality ConditionThe Classical Petz EqualityConditionProduct Additivity of Finite Classical KL DivergenceProduct Additivity of FiniteClassical KL DivergenceLog-Sum Inequality and Joint Convexity on General SupportLog-Sum Inequality and JointConvexity on General SupportClassical Data Processing on General SupportClassical Data Processing onGeneral SupportRenyi Divergence: Order One LimitRenyi Divergence: Order OneLimit
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Lean sourceResearch workspace
Status
Closed
Depth
0
Layer
D5/S3
Domain
Divergence
Node ID
D5/S3/Divergence/ClassicalDPI
Repository path
D5/S3/Divergence/ClassicalDPI.lean
Truth release
sha256:c0d04258d27972c1cf58485e21d64dbcbe336405346ba95133913c64ba2856aa
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745bf90812f7175f83e1235688249f9495f23bfc
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143bc6c9ab9054c406f0cdd7f3b296eb38768b5c

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