The Stochastic Occupation Kernel Method for System Identification
Fuente:
arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866917702900121600 |
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| author | Wells, Michael Lahouel, Kamel Jedynak, Bruno |
| author_facet | Wells, Michael Lahouel, Kamel Jedynak, Bruno |
| contents | The method of occupation kernels has been used to learn ordinary differential equations from data in a non-parametric way. We propose a two-step method for learning the drift and diffusion of a stochastic differential equation given snapshots of the process. In the first step, we learn the drift by applying the occupation kernel algorithm to the expected value of the process. In the second step, we learn the diffusion given the drift using a semi-definite program. Specifically, we learn the diffusion squared as a non-negative function in a RKHS associated with the square of a kernel. We present examples and simulations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_15661 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Stochastic Occupation Kernel Method for System Identification Wells, Michael Lahouel, Kamel Jedynak, Bruno Machine Learning Systems and Control The method of occupation kernels has been used to learn ordinary differential equations from data in a non-parametric way. We propose a two-step method for learning the drift and diffusion of a stochastic differential equation given snapshots of the process. In the first step, we learn the drift by applying the occupation kernel algorithm to the expected value of the process. In the second step, we learn the diffusion given the drift using a semi-definite program. Specifically, we learn the diffusion squared as a non-negative function in a RKHS associated with the square of a kernel. We present examples and simulations. |
| title | The Stochastic Occupation Kernel Method for System Identification |
| topic | Machine Learning Systems and Control |
| url | https://arxiv.org/abs/2406.15661 |