# Regularized parametric system identification: a decision-theoretic formulation

arXiv: https://arxiv.org/abs/1710.04009 · HTML: https://mlsanity.com/paper/1710.04009/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Oct 2017.

## Built on by (most cited first, 1 of 1)

- [Modelling Non-Smooth Signals with Complex Spectral Structure](https://mlsanity.com/paper/2203.06997/) (2022)

## Abstract (arXiv)

Parametric prediction error methods constitute a classical approach to the identification of linear dynamic systems with excellent large-sample properties. A more recent regularized approach, inspired by machine learning and Bayesian methods, has also gained attention. Methods based on this approach estimate the system impulse response with excellent small-sample properties. In several applications, however, it is desirable to obtain a compact representation of the system in the form of a parametric model. By viewing the identification of such models as a decision, we develop a decision-theoretic formulation of the parametric system identification problem that bridges the gap between the classical and regularized approaches above. Using the output-error model class as an illustration, we show that this decision-theoretic approach leads to a regularized method that is robust to small sample-sizes as well as overparameterization.