Mixture conditional density estimation with the EM algorithm

It is well-known that training a neural network with least squares corresponds to estimating a parametrized form of the conditional average of target's given inputs. In order to approximate multi-valued mappings, e.g., those occurring in inverse problems, a mixture of conditional densities must be used. In this paper we apply the EM algorithm to fit a mixture of Gaussian conditional densities when the parameters of the mixture, i.e., priors, means, and variances are all functions of the inputs. Our method becomes an interesting alternative to previous approaches based on nonlinear optimization.