# Sample Complexity of the Sign-Perturbed Sums Method

arXiv: https://arxiv.org/abs/2409.01243 · HTML: https://mlsanity.com/paper/2409.01243/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 23 references that are in the map.
- First posted on arXiv 2 Sep 2024.

## Builds on (most cited first, 9 of 9)

- [Learning Without Mixing: Towards A Sharp Analysis of Linear System Identification](https://mlsanity.com/paper/1802.08334/) (2018)
- [A Tutorial on the Non-Asymptotic Theory of System Identification](https://mlsanity.com/paper/2309.03873/) (2023)
- [The Sample Complexity of Learning Linear Predictors with the Squared Loss](https://mlsanity.com/paper/1406.5143/) (2014)
- [Sign-Perturbed Sums: A New System Identification Approach for Constructing Exact Non-Asymptotic Confidence Regions in Linear Regression Models](https://mlsanity.com/paper/1807.08216/) (2018)
- [Perturbed Datasets Methods for Hypothesis Testing and Structure of Corresponding Confidence Sets](https://mlsanity.com/paper/1412.2352/) (2014)
- [Sign-Perturbed Sums (SPS) with Instrumental Variables for the Identification of ARX Systems - Extended Version](https://mlsanity.com/paper/1509.04774/) (2015)
- [Finite sample performance of linear least squares estimation](https://mlsanity.com/paper/1810.06380/) (2018)
- [Sample Complexity of the Sign-Perturbed Sums Identification Method: Scalar Case](https://mlsanity.com/paper/2401.15792/) (2024)
- [Non-Asymptotic State-Space Identification of Closed-Loop Stochastic Linear Systems using Instrumental Variables](https://mlsanity.com/paper/2301.12537/) (2023)

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

- [Finite Sample Analysis of Distribution-Free Confidence Ellipsoids for Linear Regression](https://mlsanity.com/paper/2409.08801/) (2024)

## Abstract (arXiv)

We study the sample complexity of the Sign-Perturbed Sums (SPS) method, which constructs exact, non-asymptotic confidence regions for the true system parameters under mild statistical assumptions, such as independent and symmetric noise terms. The standard version of SPS deals with linear regression problems, however, it can be generalized to stochastic linear (dynamical) systems, even with closed-loop setups, and to nonlinear and nonparametric problems, as well. Although the strong consistency of the method was rigorously proven, the sample complexity of the algorithm was only analyzed so far for scalar linear regression problems. In this paper we study the sample complexity of SPS for general linear regression problems. We establish high probability upper bounds for the diameters of SPS confidence regions for finite sample sizes and show that the SPS regions shrink at the same, optimal rate as the classical asymptotic confidence ellipsoids. Finally, the difference between the theoretical bounds and the empirical sizes of SPS confidence regions is investigated experimentally.