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Chow–Liu tree
In probability theory and statistics Chow–Liu tree is an efficient method for constructing a second-order product approximation of a joint probability distribution, first described in a paper by . The goals of such a decomposition, as with such Bayesian networks in general, may be either data compression or inference.
==The Chow–Liu representation==
The Chow–Liu method describes a joint probability distribution as a product of second-order conditional and marginal distributions. For example, the six-dimensional distribution might be approximated as
:
where each new term in the product introduces just one new variable, and the product can be represented as a first-order dependency tree, as shown in the figure. The Chow–Liu algorithm (below) determines which conditional probabilities are to be used in the product approximation. In general, unless there are no third-order or higher-order interactions, the Chow–Liu approximation is indeed an ''approximation'', and cannot capture the complete structure of the original distribution. provides a modern analysis of the Chow–Liu tree as a Bayesian network.
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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