Bayesian Framework for a MIMO Volterra Tensor Network

Journal article (2023)

Authors

E.M. Memmel Team Kim Batselier - Mechanical, Maritime and Materials Engineering
C.M. Menzen Team Manon Kok - Mechanical, Maritime and Materials Engineering
K. Batselier Team Kim Batselier - Mechanical, Maritime and Materials Engineering
Research Group
Team Kim Batselier (Mechanical, Maritime and Materials Engineering) (TU Delft)
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Published Date

2023

Language

English

Faculty

Mechanical, Maritime and Materials Engineering

Department

Delft Center for Systems and Control

Research Group

Team Kim Batselier

Abstract

This paper proposes a Bayesian Volterra tensor network (TN) to solve high-order discrete nonlinear multiple-input multiple-output (MIMO) Volterra system identification problems. Using a low-rank tensor network to compress all Volterra kernels at once, we avoid the exponential growth of monomials with respect to the order of the Volterra kernel. Our contribution is to introduce a Bayesian framework for the low-rank Volterra TN. Compared to the least squares solution for Volterra TNs, we include prior assumptions explicitly in the model. In particular, we show for the first time how a zero-mean prior with diagonal covariance matrix corresponds to implementing a Tikhonov regularization for the MIMO Volterra TN. Furthermore, adopting a Bayesian viewpoint enables simulations with Bayesian uncertainty bounds based on noise and prior assumptions. In addition, we demonstrate via numerical experiments how Tikhonov regularization prevents overfitting in the case of higher-rank TNs.