Equivalence of Linear Boltzmann Chains and Hidden Markov Models
David J C MacKay
Several authors have studied the relationship
between hidden Markov models and `Boltzmann chains'
with a linear or `time-sliced' architecture.
Boltzmann chains model sequences of states by
defining state-state transition energies instead
of probabilities.
In this note I demonstrate that, under the
simple condition that the state sequence has a mandatory end
state, the probability distribution assigned by a strictly
linear Boltzmann
chain is identical to that assigned by a hidden Markov model.