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NeuroCOLT
Technical Report NC-TR-95-034
Mapping
Bayesian Networks to Boltzmann Machines
Petri
Myllymäki
University of Helsinki
Finland
Abstract
We study the task of finding a maximal a posteriori (MAP) instantiation
of Bayesian network variables, given a partial value assignment as
an initial constraint. This problem is known to be NP-hard, so we
concentrate on a stochastic approximation algorithm, simulated annealing.
This stochastic algorithm can be realized as a sequential process
on the set of Bayesian network variables, where only one variable
is allowed to change at a time. Consequently, the method can become
impractically slow as the number of variables increases. We present
a method for mapping a given Bayesian network to a massively parallel
Bolztmann machine neural network architecture, in the sense that instead
of using the normal sequential simulated annealing algorithm, we can
use a massively parallel stochastic process on the Boltzmann machine
architecture. The neural network updating process provably converges
to a state which solves a given MAP task.
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