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What is joint entropy and conditional entropy?
joint entropy is the amount of information in two (or more) random variables; conditional entropy is the amount of information in one random variable given we already know the other.
What is joint entropy and mutual information?
The concept of mutual information is intimately linked to that of entropy of a random variable, a fundamental notion in information theory that quantifies the expected “amount of information” held in a random variable. Mutual Information is also known as information gain.
What is entropy theory?
In information theory, the entropy of a random variable is the average level of “information”, “surprise”, or “uncertainty” inherent in the variable’s possible outcomes. An equivalent definition of entropy is the expected value of the self-information of a variable.
How is joint entropy related to conditional entropy?
Venn diagram showing additive and subtractive relationships various information measures associated with correlated variables X and Y. The area contained by both circles is the joint entropy H(X,Y). The circle on the left (red and violet) is the individual entropy H(X), with the red being the conditional entropy H(X|Y).
How is the entropy of conditioned on measured?
In information theory, the conditional entropy (or equivocation) quantifies the amount of information needed to describe the outcome of a random variable given that the value of another random variable is known. Here, information is measured in shannons, nats, or hartleys. The entropy of conditioned on is written as .
What is the Venn diagram of conditional entropy?
Conditional entropy. Venn diagram showing additive and subtractive relationships various information measures associated with correlated variables X and Y. The area contained by both circles is the joint entropy H(X,Y). The circle on the left (red and violet) is the individual entropy H(X), with the red being the conditional entropy H(X|Y).
Which is the entropy of Y and X?
The entropy of H ( Y | X = x ) = − ∑ y ∈ Y Pr ( Y = y | X = x ) log 2 Pr ( Y = y | X = x ) . {\\displaystyle \\mathrm {H} (Y|X=x)=-\\sum _ {y\\in {\\mathcal {Y}}} {\\Pr (Y=y|X=x)\\log _ {2} {\\Pr (Y=y|X=x)}}.} may take. Also, if the above sum is taken over a sample is known in some domains as equivocation. . are independent random variables .