Rate-Optimal Non-Asymptotics for the Quadratic Prediction Error Method
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866914756274683904 |
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| author | Stamouli, Charis Ziemann, Ingvar Pappas, George J. |
| author_facet | Stamouli, Charis Ziemann, Ingvar Pappas, George J. |
| contents | We study the quadratic prediction error method -- i.e., nonlinear least squares -- for a class of time-varying parametric predictor models satisfying a certain identifiability condition. While this method is known to asymptotically achieve the optimal rate for a wide range of problems, there have been no non-asymptotic results matching these optimal rates outside of a select few, typically linear, model classes. By leveraging modern tools from learning with dependent data, we provide the first rate-optimal non-asymptotic analysis of this method for our more general setting of nonlinearly parametrized model classes. Moreover, we show that our results can be applied to a particular class of identifiable AutoRegressive Moving Average (ARMA) models, resulting in the first optimal non-asymptotic rates for identification of ARMA models. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_07937 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Rate-Optimal Non-Asymptotics for the Quadratic Prediction Error Method Stamouli, Charis Ziemann, Ingvar Pappas, George J. Statistics Theory Machine Learning Systems and Control We study the quadratic prediction error method -- i.e., nonlinear least squares -- for a class of time-varying parametric predictor models satisfying a certain identifiability condition. While this method is known to asymptotically achieve the optimal rate for a wide range of problems, there have been no non-asymptotic results matching these optimal rates outside of a select few, typically linear, model classes. By leveraging modern tools from learning with dependent data, we provide the first rate-optimal non-asymptotic analysis of this method for our more general setting of nonlinearly parametrized model classes. Moreover, we show that our results can be applied to a particular class of identifiable AutoRegressive Moving Average (ARMA) models, resulting in the first optimal non-asymptotic rates for identification of ARMA models. |
| title | Rate-Optimal Non-Asymptotics for the Quadratic Prediction Error Method |
| topic | Statistics Theory Machine Learning Systems and Control |
| url | https://arxiv.org/abs/2404.07937 |