SYSTEM AND METHOD FOR BOUNDING MEANS OF DISCRETE-VALUED DISTRIBUTIONS

The present teaching relates to method, system, medium, and implementations for characterizing data with categorical classes and the number of observations for each of the categorical classes. Each categorical class is associated with a category value. The categorical classes are arranged in a first order based on category values. A total of observations is determined based on the numbers of observations for each categorical class. A bound of the average value of the data is estimated based on the categorical classes, the total of observations, and the numbers of observations for the categorical classes in accordance with a dot product of a probability vector and a categorical class vector comprising the category values of the categorical classes.