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Machine learning techniques arise largely from statistics and also information theory. In general, entropy is a measure of uncertainty and the objective of machine learning is to minimize uncertainty. Decision tree learning algorithms use relative entropy to determine the decision rules that govern the data at each node. [34]
By analogy with information theory, it is called the relative entropy of P with respect to Q. Expressed in the language of Bayesian inference, () is a measure of the information gained by revising one's beliefs from the prior probability distribution Q to the posterior probability distribution P.
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.
It is a "one-shot" analogue of quantum relative entropy and shares many properties of the latter quantity. In the study of quantum information theory, we typically assume that information processing tasks are repeated multiple times, independently. The corresponding information-theoretic notions are therefore defined in the asymptotic limit.
In information theory, the cross-entropy between two probability distributions and , over the same underlying set of events, measures the average number of bits needed to identify an event drawn from the set when the coding scheme used for the set is optimized for an estimated probability distribution , rather than the true distribution .
The Kullback–Leibler divergence (or information divergence, information gain, or relative entropy) is a way of comparing two distributions: a "true" probability distribution , and an arbitrary probability distribution .
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. More specifically, it quantifies the " amount of information " (in units such as shannons ( bits ), nats or hartleys ) obtained about one random variable by observing the other random ...
In information theory, a double bar is commonly used: (); this is similar to, but distinct from, the notation for conditional probability, (|), and emphasizes interpreting the divergence as a relative measurement, as in relative entropy; this notation is common for the KL divergence.