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For example, the quotient rule is a consequence of the chain rule and the product rule. To see this, write the function f ( x )/ g ( x ) as the product f ( x ) · 1/ g ( x ) .
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.
The chain rule can be used to find whether they are getting closer or further apart. For example, one can consider the kinematics problem where one vehicle is heading West toward an intersection at 80 miles per hour while another is heading North away from the intersection at 60 miles per hour.
In propositional logic, hypothetical syllogism is the name of a valid rule of inference (often abbreviated HS and sometimes also called the chain argument, chain rule, or the principle of transitivity of implication). The rule may be stated:
Suppose a function f(x, y, z) = 0, where x, y, and z are functions of each other. Write the total differentials of the variables = + = + Substitute dy into dx = [() + ()] + By using the chain rule one can show the coefficient of dx on the right hand side is equal to one, thus the coefficient of dz must be zero () + = Subtracting the second term and multiplying by its inverse gives the triple ...
Backpropagation computes the gradient of a loss function with respect to the weights of the network for a single input–output example, and does so efficiently, computing the gradient one layer at a time, iterating backward from the last layer to avoid redundant calculations of intermediate terms in the chain rule; this can be derived through ...
The rule began to come under scrutiny during the Biden administration promptin ... but it has also started to diversify its supply chain, adding suppliers in Brazil and Turkey, for example, a move ...
The data processing inequality is closely related to conditional mutual information and can be proven using the chain rule. Interaction information The ...