# Decoupling multivariate functions using a non-parametric Filtered CPD approach

arXiv: https://arxiv.org/abs/2105.08518 · HTML: https://mlsanity.com/paper/2105.08518/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 May 2021.

## Built on by (most cited first, 2 of 2)

- [State-Space Kolmogorov Arnold Networks for Interpretable Nonlinear System Identification](https://mlsanity.com/paper/2506.16392/) (2025)
- [Decoupling multivariate functions using a nonparametric filtered tensor decomposition](https://mlsanity.com/paper/2205.11153/) (2022)

## Abstract (arXiv)

Black-box model structures are dominated by large multivariate functions. Usually a generic basis function expansion is used, e.g. a polynomial basis, and the parameters of the function are tuned given the data. This is a pragmatic and often necessary step considering the black-box nature of the problem. However, having identified a suitable function, there is no need to stick to the original basis. So-called decoupling techniques aim at translating multivariate functions into an alternative basis, thereby both reducing the number of parameters and retrieving underlying structure. In this work a filtered canonical polyadic decomposition (CPD) is introduced. It is a non-parametric method which is able to retrieve decoupled functions even when facing non-unique decompositions. Tackling this obstacle paves the way for a large number of modelling applications.