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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2603.19073 |
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| _version_ | 1866915875740712960 |
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| author | Simpson, Léo Baumgärtner, Katrin Köhler, Johannes Diehl, Moritz |
| author_facet | Simpson, Léo Baumgärtner, Katrin Köhler, Johannes Diehl, Moritz |
| contents | This paper presents uniform-in-time finite-sample bounds for regularized linear regression with vector-valued outputs and conditionally zero-mean subgaussian noise. By revisiting classical self-normalized martingale arguments, we obtain bounds that apply directly to multi-output regression, unlike most of the prior work. Compared to the state of the art, the new results are more general and yield tighter bounds, even for scalar-valued outputs. The mild assumptions we use allow for unknown dependencies between regressors and past noise terms, typically induced by system dynamics or feedback mechanisms. Therefore, these novel finite-sample bounds can be applied to many affine-in-parameter system identification problems, including the identification of a linear time-invariant system from full-state measurements. These new results may lead to significant improvements in stochastic learning-based controllers for safety-critical applications. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_19073 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Finite-sample bounds for multi-output system identification Simpson, Léo Baumgärtner, Katrin Köhler, Johannes Diehl, Moritz Statistics Theory Dynamical Systems This paper presents uniform-in-time finite-sample bounds for regularized linear regression with vector-valued outputs and conditionally zero-mean subgaussian noise. By revisiting classical self-normalized martingale arguments, we obtain bounds that apply directly to multi-output regression, unlike most of the prior work. Compared to the state of the art, the new results are more general and yield tighter bounds, even for scalar-valued outputs. The mild assumptions we use allow for unknown dependencies between regressors and past noise terms, typically induced by system dynamics or feedback mechanisms. Therefore, these novel finite-sample bounds can be applied to many affine-in-parameter system identification problems, including the identification of a linear time-invariant system from full-state measurements. These new results may lead to significant improvements in stochastic learning-based controllers for safety-critical applications. |
| title | Finite-sample bounds for multi-output system identification |
| topic | Statistics Theory Dynamical Systems |
| url | https://arxiv.org/abs/2603.19073 |