Local Computation with Gaussian Potentials
نویسنده
چکیده
Gaussian or multivariate normal distributions are very popular and important probability models. Gaussian potentials [5] are multivariate normal density functions. Such a distribution is often given as a product of conditional Gaussian densities, which are more general than Gaussian potentials. These are related to Gaussian hints [11] and Gaussian belief functions [9, 10]. Gaussian potentials, which form a cancellative semigroup, can be embedded into a valuation algebra of pairs. In this separative extension, marginalization may be defined only partially. Gaussian potentials form a cancellative semigroup, so families of conditional Gaussian distributions are in the separative extension of Gaussian potentials. Since combination of Gaussian potentials is matrix additition of concentration matrices, division is substraction of concentration matrices, which leads to a new representation of a pair of two concentration matrices by a symmetric matrix, and to a valuation of symmetric Gaussian potentials. With this extension valuation algebra, local computation can be performed on join trees. Construction sequences cover factorizations of Gaussian potentials into conditional Gaussian potentials.
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