Learning in presence of input noise using the stochastic EM algorithm
Hichem Snoussi · AIP conference proceedings · 2003
Most learning algorithms rely on the assumption that the input training data contains no noise or uncertainty. However, when collecting data under an identification experiment it may not be possible to avoid noise when measuring the input. The use of the errors‐in‐variable model to describe the data in this case is more appropriate. However, learning based on maximum likelihood estimation is far from straightforward because of the high number of unknown parameters. In this paper, to overcome the problems associated to the estimation with high number of unknown parameters, the nonlinear errors‐in‐variable estimation problem is treated under a Bayesian formulation. In order to compute the necessary maximum a posteriori estimate we use the restoration maximization algorithms where the true but unknown training inputs are treated as hidden variables. In order to accelerate the convergence of the algorithm a modified version of the stochastic EM algorithm is proposed. A simulation example on learning a nonlinear parametric function and an example on learning feedforward neural networks are presented to illustrate the effectiveness of the proposed learning method.