Twice-universal simulation of Markov sources and individual sequences

Authors:
Álvaro Martín;Neri Merhav;Gadiel Seroussi;Marcelo J. Weinberger
Affiliations:
Instituto de Computación, Universidad de la República, Montevideo, Uruguay;Department of Electrlcal Engineering, Technion-Israel, Institute of Technology, Haifa, Israel;Hewlett-Packard Laboratories, Palo Alto, CA and Universidad de la República, Montevideo, Uruguay;Hewlett-Packard Laboratories, Palo Alto, CA
Venue:
IEEE Transactions on Information Theory
Year:
2010

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Abstract

The problem of universal simulation given a training sequence is studied both in a stochastic setting and for individual sequences. In the stochastic setting, the training sequence is assumed to be emitted by a Markov source of unknown order, extending previous work where the order is assumed known and leading to the notion of twice-universal simulation. A simulation scheme, which partitions the set of sequences of a given length into classes, is proposed for this setting and shown to be asymptotically optimal. This partition extends the notion of type classes to the twice-universal setting. In the individual sequence scenario, the same simulation scheme is shown to generate sequences which are statistically similar, in a strong sense, to the training sequence, for statistics of any order, while essentially maximizing the uncertainty on the output.