On universal simulation of information sources using training data

We consider a universal version of the problem of simulation, where the unknown source to be simulated is represented by a finite training sequence. While in the ordinary simulation problem, the number of random bits per symbol must exceed the entropy H of the source in order to simulate it faithfully, in universal simulation, where the probability law of the target source is always perfectly preserved, H random bits per symbol are still needed to essentially eliminate the statistical dependency between the training sequence and the output sequence.