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In information theory, the conditional entropy 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 violet is the mutual information (;) . Venn diagram of information theoretic measures for three variables x, y , and z . Each circle represents an individual entropy : H ( x ) {\displaystyle H(x)} is the lower left circle, H ( y ) {\displaystyle H(y)} the lower right, and H ( z ) {\displaystyle H(z)} is the ...
English: This diagram shows the relation between the entropies of two random variables X and Y and their mutual information, joint entropy and relative (conditional) entropies. Deutsch: Dieses Diagramm visualisiert die Beziehung zwischen den Entropien zweier Zufallsvariablen X und Y und ihrer gemeinsamen Information, Verbundentropie und ...
The circle on the right (blue and violet) is (), with the blue being (). The violet is the mutual information I ( X ; Y ) {\displaystyle \operatorname {I} (X;Y)} . In probability theory and information theory , the mutual information ( MI ) of two random variables is a measure of the mutual dependence between the two variables.
A misleading [1] Venn diagram showing additive, and subtractive relationships between 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 ...
Although, in both cases, mutual information expresses the number of bits of information common to the two sources in question, the analogy does not imply identical properties; for example, differential entropy may be negative. The differential analogies of entropy, joint entropy, conditional entropy, and mutual information are defined as follows:
The relatively high value of entropy () = (1 is the optimal value) suggests that the root node is highly impure and the constituents of the input at the root node would look like the leftmost figure in the above Entropy Diagram. However, such a set of data is good for learning the attributes of the mutations used to split the node.
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