# Regularization and Bayesian Learning in Dynamical Systems: Past, Present and Future

arXiv: https://arxiv.org/abs/1511.01543 · HTML: https://mlsanity.com/paper/1511.01543/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Nov 2015.

## Built on by (most cited first, 4 of 4)

- [Deep networks for system identification: a Survey](https://mlsanity.com/paper/2301.12832/) (2023)
- [Robust Bayesian Subspace Identification for Small Data Sets](https://mlsanity.com/paper/2212.14132/) (2022)
- [Maximum likelihood inference for high-dimensional problems with multiaffine variable relations](https://mlsanity.com/paper/2409.03495/) (2024)
- [XMSE-Aware Adaptive Empirical Bayes Estimation](https://mlsanity.com/paper/2606.26975/) (2026)

## Abstract (arXiv)

Regularization and Bayesian methods for system identification have been repopularized in the recent years, and proved to be competitive w.r.t. classical parametric approaches. In this paper we shall make an attempt to illustrate how the use of regularization in system identification has evolved over the years, starting from the early contributions both in the Automatic Control as well as Econometrics and Statistics literature. In particular we shall discuss some fundamental issues such as compound estimation problems and exchangeability which play and important role in regularization and Bayesian approaches, as also illustrated in early publications in Statistics. The historical and foundational issues will be given more emphasis (and space), at the expense of the more recent developments which are only briefly discussed. The main reason for such a choice is that, while the recent literature is readily available, and surveys have already been published on the subject, in the author's opinion a clear link with past work had not been completely clarified.