MINLIP for the identification of monotone Wiener systems

This paper studies the MINLIP estimator for the identification of Wiener systems consisting of a sequence of a linear FIR dynamical model, and a monotonically increasing (or decreasing) static function. Given TT observations, this algorithm boils down to solving a convex quadratic program with O(T)O(T) variables and inequality constraints, implementing an inference technique which is based entirely on model complexity control, a technique which is dubbed as Einstein’s razor.2 This technique is proven to yield, here, almost consistent estimates in case the given data is suitably rich (local Persistently Exciting of sufficient order), and if the samples obey a ‘true’ monotone Wiener system satisfying some regularity conditions. It is then indicated how to extend the method in order to cope with noisy data, and empirical evidence is given in order to support the claim of efficiency.