Papers by Mihaela Erbiceanu
Boltzmann learning underlies an artificial neural network model known as the Boltzmann machine th... more Boltzmann learning underlies an artificial neural network model known as the Boltzmann machine that extends and improves upon the Hopfield network model. Boltzmann machine model uses stochastic binary units and allows for the existence of hidden units to represent latent variables. When subjected to reducing noise via simulated annealing and allowing uphill steps via Metropolis algorithm, the training algorithm increases the chances that, at thermal equilibrium, the network settles on the best distribution of parameters. The existence of equilibrium distribution for an asynchronous Boltzmann machine is analyzed with respect to temperature. Two families of learning algorithms, which correspond to two different approaches to compute the statistics required for learning, are presented. The learning algorithms based only on stochastic approximations are traditionally slow. When variational approximations of the free energy are used, like the mean field approximation or the Bethe approximation, the performance of learning improves considerably. The principal contribution of the present study is to provide, from a rigorous mathematical perspective, a unified framework for these two families of learning algorithms in asynchronous Boltzmann machines.
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Papers by Mihaela Erbiceanu