Addendum to “On Universal Simulation of Information Sources Using Training Data”

In a recent paper [1] , we studied the problem of universal simulation of an unknown information source of a certain parametric family, given a training sequence from that source and given a limited budget of purely random bits. The goal was to generate another random sequence (of the same length or shorter), whose probability law is identical to that of the given training sequence, but with minimum statistical dependency (minimum mutual information) between the input training sequence and the output sequence. In this addendum, we point out a concrete optimal simulation scheme that is easy to implement, as opposed to the nonconstructive existence result in that paper, and we make a number of additional observations on the universal simulation problem.