Entropy and forecasting complexity of hidden Markov models, matrix product states, and observable operator models

Abstract: In a series of three papers, Jurgens and Crutchfield recently proposed a supposedly novel method to compute entropies of hidden Markov models (HMMs), discussed in detail its relationship to iterated function systems, and applied it to compute their ambiguity rates", a concept supposedly introduced by Claude Shannon. We point out that the basic formalism is not new (it is the well knownforward algorithm" for HMMs), and that all three papers have also serious other faults.