On fields of nonlinear regression models

In the context of nonlinear regression, we consider the problem of explaining a variable y from a vector x of explanatory variables and from a vector t of conditionning variables, that influences the link function between y and x. A neural based solution is proposed in the form of a field of nonlinear regression models, by which it is meant that the relation between those variables is modeled by a map from some space to a function space. This approach results in a broader class of neural models than that of perceptrons, which therefore inherits the interesting approximation theoretical properties of the latter. The interest of such a modeling is illustrated by a real-world geophysical application, namely ocean color remote sensing.