Extending entropy and mutual information to multiple genes and phenotypes

InferenceChain·arcadia

This reasoning chain explains how fundamental measures from information theory, such as joint entropy, conditional mutual information, and chain rule relationships, can be generalized from single variables to joint distributions involving several genes and phenotypes. It shows that analyzing multiple correlated traits provides more predictive value and that pleiotropy and correlation structure decrease total system entropy.

Confidence

80%

◑partialactivecomplexity: mid

Reasoning Steps (2)

Chain rule for entropy and conditional mutual information enable joint analysisStep 1

Correlation and pleiotropy reduce joint phenotypic entropyStep 2

Source

Synthesis for current paper

Connections (8)

Chain rule defines joint entropy as sum of conditional entropiesAssociation

Mutual information equals KL divergence of joint vs independent distributionsAssociation

Chain rule for mutual information gives sum of conditional valuesAssociation

Polyphenotypic analysis increases prediction accuracyAssociation

Increasing pleiotropy decreases joint phenotypic entropyAssociation

Joint phenotypic entropy less than maximal entropy when traits correlatedAssociation

Phenotype-phenotype correlation causes reduction in joint entropyAssociation

Interaction information generalizes mutual information to multiple variablesAssociation