On the Use of I-Divergence for Generating Distribution Approximations

The existence of an upper bound for the error probability as a function of I-divergences between an original and an approximating distribution is proved. Such a bound is shown to be a monotonic nondecreasing function of the I-divergences, reaching the Bayes error probability when they vanish. It has been shown that if the closeness between the original and approximating distributions is assessed by the probability of error associated with a particular two-class recognition problem in which those functions are the class conditional distributions, then the best upper bound for such probability is ¿ regardless of the value of the I-divergences between them. Approaching the approximation problem from a rather different viewpoint, this correspondence considers the problem of a two-class discrete measurement classification where the original distributions are replaced by approximations, and its effects on the probability of error. The corresponding analysis is presented in detail.