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 randomvariables is observed, ICA can be used for regression, i.e. to predict the missing observations. In this paper, we show that the resulting regression is closely related to regression by a multi-layer perceptron (MLP). In fact, if linear dependencies arefirst 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 thevalues of the independent components, and the sigmoid nonlinearities are obtained from the probability densities of the independent components.
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