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The violet is the mutual information . 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 entropy of conditioned on is written as .
where () and () are the marginal entropies, () and () are the conditional entropies, and (,) is the joint entropy of and . Notice the analogy to the union, difference, and intersection of two sets: in this respect, all the formulas given above are apparent from the Venn diagram reported at the beginning of the article.
The conditional mutual informations , and are represented by the yellow, cyan, and magenta regions, respectively. In probability theory, particularly information theory, the conditional mutual information[1][2] is, in its most basic form, the expected value of the mutual information of two random variables given the value of a third.
In information theory, the entropy of a random variable quantifies the average level of uncertainty or information associated with the variable's potential states or possible outcomes. This measures the expected amount of information needed to describe the state of the variable, considering the distribution of probabilities across all potential ...
Information gain (decision tree) In information theory and machine learning, information gain is a synonym for Kullback–Leibler divergence; the amount of information gained about a random variable or signal from observing another random variable. However, in the context of decision trees, the term is sometimes used synonymously with mutual ...
Definition. The cross-entropy of the distribution relative to a distribution over a given set is defined as follows: {\displaystyle H (p,q)=-\operatorname {E} _ {p} [\log q],} where is the expected value operator with respect to the distribution . The definition may be formulated using the Kullback–Leibler divergence , divergence of from ...
The Fisher information is a way of measuring the amount of information that an observable random variable carries about an unknown parameter upon which the probability of depends. Let be the probability density function (or probability mass function) for conditioned on the value of . It describes the probability that we observe a given outcome ...
Uncertainty coefficient. In statistics, the uncertainty coefficient, also called proficiency, entropy coefficient or Theil's U, is a measure of nominal association. It was first introduced by Henri Theil [citation needed] and is based on the concept of information entropy.