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In this situation, the chain rule represents the fact that the derivative of f ∘ g is the composite of the derivative of f and the derivative of g. This theorem is an immediate consequence of the higher dimensional chain rule given above, and it has exactly the same formula. The chain rule is also valid for Fréchet derivatives in Banach spaces.
This rule allows one to express a joint probability in terms of only conditional probabilities. [4] The rule is notably used in the context of discrete stochastic processes and in applications, e.g. the study of Bayesian networks, which describe a probability distribution in terms of conditional probabilities.
A more general definition of conditional mutual information, applicable to random variables with continuous or other arbitrary distributions, will depend on the concept of regular conditional probability.
The scope of the term "crusade" first referred to military expeditions undertaken by European Christians in the 11th, 12th, and 13th centuries to the Holy Land. The conflicts to which the term is applied has been extended to include other campaigns initiated, supported and sometimes directed by the Roman Catholic Church against pagans, heretics ...
Francis Drake's circumnavigation, also known as Drake's Raiding Expedition, was an important historical maritime event that took place between 15 December 1577 and 26 September 1580. The expedition was authorised by Queen Elizabeth I and consisted of five ships led by Francis Drake .
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The basic idea of the chain rule is pretty easy to explain in words: The best linear approximation of the composition is the composition of the best linear approximations. Every special case of the chain rule, more or less expresses this fact in various situations, with a wide variety of abstraction or concreteness.