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Conditional Independence

Statistical independence and conditional independence (CI) are important concepts in statistics, artificial intelligence, and related fields. Let X, Y, and Z denote three sets of random variables, and let P denote their probability distribution or density functions. X and Y are conditionally independent given Z, denoted by XY | Z, if and only if P(X, Y | Z) = P(X | Z) P(Y | Z). It reflects the fact that given the values of Z, further knowing the values of X does not provide any additional information about Y. Generally speaking, such a CI relationship allows us to drop X when constructing a probabilistic model for Y with (X, Z), resulting in a parsimonious representation. Moreover, independence and CI play a central role ...

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