Probabilistic distances between finite-state finite-alphabet hidden Markov models

2004 ◽  
Author(s):  
Li Xie ◽  
V.A. Ugrinovskii ◽  
I.R. Petersen
Keyword(s):  
Hidden Markov Models ◽  
Markov Models ◽  
Hidden Markov ◽  
Finite Alphabet ◽  
Probabilistic Distances ◽  
Finite State

scholarly journals On learning finite-state quantum sources

2012 ◽  
Vol 12 (1&2) ◽  
pp. 105-118
Author(s):  
Brendan Juba
Keyword(s):  
Hidden Markov Models ◽  
Learning Theory ◽  
Markov Models ◽  
Hidden Markov ◽  
Computational Learning Theory ◽  
Computational Learning ◽  
Finite State ◽  
Quantum Generator ◽  
State Of Affairs ◽  
Open Question

We examine the complexity of learning the distributions produced by finite-state quantum sources. We show how prior techniques for learning hidden Markov models can be adapted to the {\em quantum generator} model to find that the analogous state of affairs holds: information-theoretically, a polynomial number of samples suffice to approximately identify the distribution, but computationally, the problem is as hard as learning parities with noise, a notorious open question in computational learning theory.

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