Global Boltzmann perceptron network for online learning of conditional distributions

This paper proposes a backpropagation-based feedforward neural network for learning probability distributions of outputs conditioned on inputs using incoming input-output samples only. The backpropagation procedure is shown to locally minimize the Kullback-Leibler measure in an expected sense. The procedure is enhanced to facilitate boundedness of weights and exploration of the search space to reach a global minimum. Weak convergence theory is employed to show that the longterm behavior of the resulting algorithm can be approximated by that of a stochastic differential equation, whose invariant distributions are concentrated around the global minima of the Kullback-Leibler measure within a region of interest. Simulation studies on problems involving samples arriving from a mixture of labeled densities and the well-known Iris data problem demonstrate the speed and accuracy of the proposed procedure.