Improving variational methods via pairwise linear response identities

摘要: Inference methods are often formulated as variational approximations: these approximations allow easy evaluation of statistics by marginalization or linear response, but estimates can be inconsistent. We show that introducing constraints on covariance, one ensure consistency response with the parameters, and in so doing inference marginal probability distributions is improved. For Bethe approximation its generalizations, improvements achieved simple choices constraints. The presented frameworks; iterative procedures related to message passing provided for finding minima.