Generator Identification for Linear SDEs with Additive and Multiplicative Noise
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arXiv
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| Auteurs principaux: | , , , , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866910304067125248 |
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| author | Wang, Yuanyuan Geng, Xi Huang, Wei Huang, Biwei Gong, Mingming |
| author_facet | Wang, Yuanyuan Geng, Xi Huang, Wei Huang, Biwei Gong, Mingming |
| contents | In this paper, we present conditions for identifying the generator of a linear stochastic differential equation (SDE) from the distribution of its solution process with a given fixed initial state. These identifiability conditions are crucial in causal inference using linear SDEs as they enable the identification of the post-intervention distributions from its observational distribution. Specifically, we derive a sufficient and necessary condition for identifying the generator of linear SDEs with additive noise, as well as a sufficient condition for identifying the generator of linear SDEs with multiplicative noise. We show that the conditions derived for both types of SDEs are generic. Moreover, we offer geometric interpretations of the derived identifiability conditions to enhance their understanding. To validate our theoretical results, we perform a series of simulations, which support and substantiate the established findings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_19491 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Generator Identification for Linear SDEs with Additive and Multiplicative Noise Wang, Yuanyuan Geng, Xi Huang, Wei Huang, Biwei Gong, Mingming Statistics Theory Machine Learning In this paper, we present conditions for identifying the generator of a linear stochastic differential equation (SDE) from the distribution of its solution process with a given fixed initial state. These identifiability conditions are crucial in causal inference using linear SDEs as they enable the identification of the post-intervention distributions from its observational distribution. Specifically, we derive a sufficient and necessary condition for identifying the generator of linear SDEs with additive noise, as well as a sufficient condition for identifying the generator of linear SDEs with multiplicative noise. We show that the conditions derived for both types of SDEs are generic. Moreover, we offer geometric interpretations of the derived identifiability conditions to enhance their understanding. To validate our theoretical results, we perform a series of simulations, which support and substantiate the established findings. |
| title | Generator Identification for Linear SDEs with Additive and Multiplicative Noise |
| topic | Statistics Theory Machine Learning |
| url | https://arxiv.org/abs/2310.19491 |