Local Factorization of Functions
This paper is concerned with the notion of a local factorization of a function where we are mostly interested in the special case that this function is a probability distribution. We introduce the notions of local independence and of the local Kullback-Leibler divergence. We introduce a specific approximate local factorization. The number of terms required in the approximation is linear in the number of input dimensions and the approximation does not require the calculation of higher derivatives (as in a Taylor expansion) and is not limited to approximations near the mode of a function. We provide examples where we believe the approximation might be useful as in the approximate calculation of certain integrals.