Accelerated learning in Boltzmann Machines using mean field theory

Abstract

The learning process in Boltzmann Machines is computationally intractible. We present a new approximate learning algorithm for Boltzmann Machines, which is based on mean field theory and the linear response theorem. The computational complexity of the algorithm is cubic in the number of neurons.

In the absence of hidden units, we show how the weights can be directly computed from the fixed point equation of the learning rules. We show that the solutions of this method are close to the optimal and give a significant improvement over the naive mean field approach.