Massively Parallel Probabilistic Reasoning with Boltzmann Machines

摘要

We present a method for mapping a given Bayesian network to a Boltzmann machine architecture, in the sense that the the updating process of the resulting Boltzmann machine model probably converges to a state which can be mapped back to a maximum a posteriori (MAP) probability state in the probability distribution represented by the Bayesian network. The Boltzmann machine model can be implemented efficiently on massively parallel hardware, since the resulting structure can be divided into two separate clusters where all the nodes in one cluster can be updated simultaneously. This means that the proposed mapping can be used for providing Bayesian network models with a massively parallel probabilistic reasoning module, capable of finding the MAP states in a computationally efficient manner. From the neural network point of view, the mapping from a Bayesian network to a Boltzmann machine can be seen as a method for automatically determining the structure and the connection weights of a Boltzmann machine by incorporating high-level, probabilistic information directly into the neural network architecture, without recourse to a time-consuming and unreliable learning process.