MINLIP for the Identification of Monotone Wiener Systems

TL;DR

This paper introduces MINLIP, a convex quadratic programming approach for identifying monotone Wiener systems, demonstrating near consistency in noise-free conditions and contrasting its performance with other methods.

Contribution

The paper presents a novel, model complexity-based inference method for Wiener systems that does not rely on classical linearization or stochastic assumptions.

Findings

Estimator is almost consistent without noise under certain conditions

Method extends to noisy data scenarios

Empirical results compare favorably with recent techniques

Abstract

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 $T$ observations, this algorithm boils down to solving a convex quadratic program with $O(T)$ variables and inequality constraints, implementing an inference technique which is based entirely on model complexity control. The resulting estimates of the linear submodel are found to be almost consistent when no noise is present in the data, under a condition of smoothness of the true nonlinearity and local Persistency of Excitation (local PE) of the data. This result is novel as it does not rely on classical tools as a 'linearization' using a Taylor decomposition, nor exploits stochastic properties of the data. It is indicated how to extend the method to cope with noisy data, and empirical evidence contrasts performance of the estimator against other recently proposed techniques.