# Estimation Sample Complexity of a Class of Nonlinear Continuous-time Systems

arXiv: https://arxiv.org/abs/2312.05382 · HTML: https://mlsanity.com/paper/2312.05382/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 5 of its 46 references that are in the map.
- First posted on arXiv 8 Dec 2023.

## Builds on (most cited first, 5 of 5)

- [Active Learning for Nonlinear System Identification with Guarantees](https://mlsanity.com/paper/2006.10277/) (2020)
- [Statistical Learning Theory for Control: A Finite Sample Perspective](https://mlsanity.com/paper/2209.05423/) (2022)
- [A Tutorial on the Non-Asymptotic Theory of System Identification](https://mlsanity.com/paper/2309.03873/) (2023)
- [Numerical differentiation of noisy data: A unifying multi-objective optimization framework](https://mlsanity.com/paper/2009.01911/) (2020)
- [A Tutorial on Concentration Bounds for System Identification](https://mlsanity.com/paper/1906.11395/) (2019)

## Abstract (arXiv)

We present a method of parameter estimation for large class of nonlinear systems, namely those in which the state consists of output derivatives and the flow is linear in the parameter. The method, which solves for the unknown parameter by directly inverting the dynamics using regularized linear regression, is based on new design and analysis ideas for differentiation filtering and regularized least squares. Combined in series, they yield a novel finite-sample bound on mean absolute error of estimation.