# A novel Multiplicative Polynomial Kernel for Volterra series identification

arXiv: https://arxiv.org/abs/1905.07960 · HTML: https://mlsanity.com/paper/1905.07960/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 May 2019.

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

- [Model-Based Policy Search Using Monte Carlo Gradient Estimation with Real Systems Application](https://mlsanity.com/paper/2101.12115/) (2021)
- [Model-based Policy Search for Partially Measurable Systems](https://mlsanity.com/paper/2101.08740/) (2021)

## Abstract (arXiv)

Volterra series are especially useful for nonlinear system identification, also thanks to their capability to approximate a broad range of input-output maps. However, their identification from a finite set of data is hard, due to the curse of dimensionality. Recent approaches have shown how regularized kernel-based methods can be useful for this task. In this paper, we propose a new regularization network for Volterra models identification. It relies on a new kernel given by the product of basic building blocks. Each block contains some unknown parameters that can be estimated from data using marginal likelihood optimization. In comparison with other algorithms proposed in the literature, numerical experiments show that our approach allows to better select the monomials that really influence the system output, much increasing the prediction capability of the model.