Local probabilistic approximations for incomplete data

In this paper we introduce a generalization of the local approximation called a local probabilistic approximation. Our novel idea is associated with a parameter (probability) α. If α = 1, the local probabilistic approximation becomes a local lower approximation; for small α, it becomes a local upper approximation. The main objective of this paper is to test whether proper local probabilistic approximations (different from local lower and upper approximations) are better than ordinary local lower and upper approximations. Our experimental results, based on ten-fold cross validation, show that all depends on a data set: for some data sets proper local probabilistic approximations are better than local lower and upper approximations; for some data sets there is no difference, for yet other data sets proper local probabilistic approximations are worse than local lower and upper approximations.