Decoupling multivariate functions using a nonparametric filtered tensor decomposition. (1st November 2022) - Decuyper, Jan; Tiels, Koen; Weiland, Siep; Runacres, Mark C.; Schoukens, Johan
Abstract: Multivariate functions emerge naturally in a wide variety of data-driven models. Popular choices are expressions in the form of basis expansions or neural networks. While highly effective, the resulting functions tend to be hard to interpret, in part because of the large number of required parameters. Decoupling techniques aim at providing an alternative representation of the nonlinearity. The so-called decoupled form is often a more efficient parameterisation of the relationship while being highly structured, favouring interpretability. In this work two new algorithms, based on filtered tensor decompositions of first order derivative information are introduced. The method returns nonparametric estimates of smooth decoupled functions. Direct applications are found in, i.a. the fields of nonlinear system identification and machine learning. Highlights: An introduction to decoupling nonlinear multivariate functions based on first-order information, i.e. obtaining efficiently parameterised functions with increased interpretability. Two novel nonparametric approaches to obtain decoupled functions. A case study demonstrating the benefits of decoupling large multivariate polynomials. A case study demonstrating the benefits of decoupling artificial neural networks. A case study demonstrating the potential of decoupling single-output NARX models.