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In probability theory, the chain rule [1] (also called the general product rule [2] [3]) describes how to calculate the probability of the intersection of, not necessarily independent, events or the joint distribution of random variables respectively, using conditional probabilities.
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The chain rule [citation needed] for Kolmogorov complexity is an analogue of the chain rule for information entropy, which states: (,) = + (|)That is, the combined randomness of two sequences X and Y is the sum of the randomness of X plus whatever randomness is left in Y once we know X.
Probability theory or probability calculus is the branch of mathematics concerned with probability. Although there are several different probability interpretations , probability theory treats the concept in a rigorous mathematical manner by expressing it through a set of axioms .
The certainty that is adopted can be described in terms of a numerical measure, and this number, between 0 and 1 (where 0 indicates impossibility and 1 indicates certainty) is called the probability. Probability theory is used extensively in statistics, mathematics, science and philosophy to draw conclusions about the likelihood of potential ...
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In probability theory, particularly information theory, the conditional mutual information [1] [2] is, in its most basic form, the expected value of the mutual information of two random variables given the value of a third.
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.