Uncertainty quantification of data-driven output predictors in the output error setting
Abstract
We study output prediction for LTI systems using only input-output data, without identifying a parametric model. Prior methods rely on projecting recent signal data onto a Hankel matrix built from offline data, but this becomes inaccurate in the presence of noise. While low-rank approximations like truncated SVD are used to mitigate noise, their effect on prediction accuracy remains unclear. We derive two upper bounds on the prediction error under small noise assumptions—one using raw data, the other with low-rank approximations. Our bounds require only noisy measurements and known system order. Simulations confirm the bounds’ linear decay with noise level.
Primary Faculty Mentor Name
Kathryn Hinkelman
Status
Graduate
Student College
College of Engineering and Mathematical Sciences
Program/Major
Electrical Engineering
Primary Research Category
Engineering and Math Science
Uncertainty quantification of data-driven output predictors in the output error setting
We study output prediction for LTI systems using only input-output data, without identifying a parametric model. Prior methods rely on projecting recent signal data onto a Hankel matrix built from offline data, but this becomes inaccurate in the presence of noise. While low-rank approximations like truncated SVD are used to mitigate noise, their effect on prediction accuracy remains unclear. We derive two upper bounds on the prediction error under small noise assumptions—one using raw data, the other with low-rank approximations. Our bounds require only noisy measurements and known system order. Simulations confirm the bounds’ linear decay with noise level.
