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Information theory is based on probability theory and statistics, where quantified information is usually described in terms of bits. Information theory often concerns itself with measures of information of the distributions associated with random variables.
In the view of Jaynes (1957), [19] thermodynamic entropy, as explained by statistical mechanics, should be seen as an application of Shannon's information theory: the thermodynamic entropy is interpreted as being proportional to the amount of further Shannon information needed to define the detailed microscopic state of the system, that remains ...
The mathematical theory of information is based on probability theory and statistics, and measures information with several quantities of information. The choice of logarithmic base in the following formulae determines the unit of information entropy that is used.
The principle of maximum entropy is useful explicitly only when applied to testable information. Testable information is a statement about a probability distribution whose truth or falsity is well-defined. For example, the statements the expectation of the variable is 2.87. and + >
In information theory, Pinsker's inequality, named after its inventor Mark Semenovich Pinsker, is an inequality that bounds the total variation distance (or statistical distance) in terms of the Kullback–Leibler divergence. The inequality is tight up to constant factors. [1]
Some of the oldest methods of telecommunications implicitly use many of the ideas that would later be quantified in information theory. Modern telegraphy, starting in the 1830s, used Morse code, in which more common letters (like "E", which is expressed as one "dot") are transmitted more quickly than less common letters (like "J", which is expressed by one "dot" followed by three "dashes").
Information theory, developed by Claude E. Shannon in 1948, defines the notion of channel capacity and provides a mathematical model by which it may be computed. The key result states that the capacity of the channel, as defined above, is given by the maximum of the mutual information between the input and output of the channel, where the ...
The expected value of the information gain is the mutual information (;) of and – i.e. the reduction in the entropy of achieved by learning the state of the random variable . In machine learning, this concept can be used to define a preferred sequence of attributes to investigate to most rapidly narrow down the state of X .