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The entropy rate of a data source is the average number of bits per symbol needed to encode it. Shannon's experiments with human predictors show an information rate between 0.6 and 1.3 bits per character in English; [21] the PPM compression algorithm can achieve a compression ratio of 1.5 bits per character in English text.
The defining expression for entropy in the theory of information established by Claude E. Shannon in 1948 is of the form: where is the probability of the message taken from the message space M, and b is the base of the logarithm used. Common values of b are 2, Euler's number e, and 10, and the unit of entropy is shannon (or bit) for b = 2, nat ...
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 ...
Information theory. Information theory is the mathematical study of the quantification, storage, and communication of information. The field was established and put on a firm footing by Claude Shannon in the 1940s, [1] though early contributions were made in the 1920s through the works of Harry Nyquist and Ralph Hartley.
Quantities of information. A misleading [1] information diagram showing additive and subtractive relationships among Shannon 's basic quantities of information for correlated variables and . The area contained by both circles is the joint entropy . The circle on the left (red and violet) is the individual entropy , with the red being the ...
Information gain ratio. In decision tree learning, information gain ratio is a ratio of information gain to the intrinsic information. It was proposed by Ross Quinlan, [1] to reduce a bias towards multi-valued attributes by taking the number and size of branches into account when choosing an attribute. [2]
The joint information is equal to the mutual information plus the sum of all the marginal information (negative of the marginal entropies) for each particle coordinate. Boltzmann's assumption amounts to ignoring the mutual information in the calculation of entropy, which yields the thermodynamic entropy (divided by the Boltzmann constant).
Kullback–Leibler divergence. In mathematical statistics, the Kullback–Leibler (KL) divergence (also called relative entropy and I-divergence[1]), denoted , is a type of statistical distance: a measure of how one reference probability distribution P is different from a second probability distribution Q. [2][3] Mathematically, it is defined as.