Regression using independent component analysis, and its connection to multi-layer perceptrons

The data model of independent component analysis (ICA) gives a multivariate probability density that describes many kinds of sensory data better than classical models like Gaussian densities or Gaussian mixtures. When only a subset of the random variables is observed, ICA can be used for regression, i.e. to predict the missing observations. We show that the resulting regression is closely related to regression by a multi-layer perceptron (MLP). In fact, if linear dependencies are first removed from the data, regression by ICA is, as a first-order approximation, equivalent to regression by MLP. This result gives a new interpretation of the elements of the MLP: the outputs of the hidden layer neurons are related to estimates of the values of the independent components, and the sigmoid nonlinearities are obtained from the probability densities of the independent components