Retention and Maximization of Information in Data Reduction

This paper considers the following problem: to minimize, with respect to a class of reductions satisfying some requirements as regards “capacities,” etc., the Bayesian or average risk which increases in data reduction, or to find a simple criterion allowing us to decide whether the drop in the quality of the solution for a given reduction is permissible. The paper offers an estimate of the increase in the average risk due to data reduction in terms of the average number of observations and the generalized Shannon entropy of individual observations.