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Despite the foregoing, there is a difference between the two quantities. The information entropy Η can be calculated for any probability distribution (if the "message" is taken to be that the event i which had probability p i occurred, out of the space of the events possible), while the thermodynamic entropy S refers to thermodynamic probabilities p i specifically.
The information gain in decision trees (,), which is equal to the difference between the entropy of and the conditional entropy of given , quantifies the expected information, or the reduction in entropy, from additionally knowing the value of an attribute . The information gain is used to identify which attributes of the dataset provide the ...
Grammatical Man: Information, Entropy, Language, and Life is a 1982 book written by Jeremy Campbell, then Washington correspondent for the Evening Standard. [1] The book examines the topics of probability, information theory, cybernetics, genetics, and linguistics. Information processes are used to frame and examine all of existence, from the ...
The base of the logarithm is not important, as long as the same one is used consistently: Change of base merely results in a rescaling of the entropy. Information theorists may prefer to use base 2 in order to express the entropy in bits; mathematicians and physicists often prefer the natural logarithm, resulting in a unit of "nat"s for the ...
An information diagram is a type of Venn diagram used in information theory to illustrate relationships among Shannon's basic measures of information: entropy, joint entropy, conditional entropy and mutual information. [1] [2] Information
The mutual information is used to learn the structure of Bayesian networks/dynamic Bayesian networks, which is thought to explain the causal relationship between random variables, as exemplified by the GlobalMIT toolkit: [37] learning the globally optimal dynamic Bayesian network with the Mutual Information Test criterion.
The Gaussian or normal probability distribution plays an important role in the relationship between variance and entropy: it is a problem of the calculus of variations to show that this distribution maximizes entropy for a given variance, and at the same time minimizes the variance for a given entropy.
Ludwig Boltzmann defined entropy as a measure of the number of possible microscopic states (microstates) of a system in thermodynamic equilibrium, consistent with its macroscopic thermodynamic properties, which constitute the macrostate of the system. A useful illustration is the example of a sample of gas contained in a container.