Maximum-entropy approximations of stochastic nonlinear transductions: an extension of the Wiener theory

We consider the description of a nonlinear stochastic transduction in terms of its input/output distribution. We construct a sequence of approximating maximum-entropy estimates from a finite set of input/output observations. This procedure extends the Wiener theory to the analysis of nonlinear stochastic transducers and to the analysis of transducers with multiple outputs but an inaccessible input.