Mixed moving average field guided learning for spatio-temporal data
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866913455470018560 |
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| author | Curato, Imma Valentina Furat, Orkun Proietti, Lorenzo Stroeh, Bennet |
| author_facet | Curato, Imma Valentina Furat, Orkun Proietti, Lorenzo Stroeh, Bennet |
| contents | Influenced mixed moving average fields are a versatile modeling class for spatio-temporal data. However, their predictive distribution is not generally known. Under this modeling assumption, we define a novel spatio-temporal embedding and a theory-guided machine learning approach that employs a generalized Bayesian algorithm to make ensemble forecasts. We use Lipschitz predictors and determine fixed-time and any-time PAC Bayesian bounds in the batch learning setting. Performing causal forecast is a highlight of our methodology as its potential application to data with spatial and temporal short and long-range dependence. We then test the performance of our learning methodology by using linear predictors and data sets simulated from a spatio-temporal Ornstein-Uhlenbeck process. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2301_00736 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Mixed moving average field guided learning for spatio-temporal data Curato, Imma Valentina Furat, Orkun Proietti, Lorenzo Stroeh, Bennet Machine Learning Statistics Theory 60E07, 60E15, 60G25, 60G60, 62C10 Influenced mixed moving average fields are a versatile modeling class for spatio-temporal data. However, their predictive distribution is not generally known. Under this modeling assumption, we define a novel spatio-temporal embedding and a theory-guided machine learning approach that employs a generalized Bayesian algorithm to make ensemble forecasts. We use Lipschitz predictors and determine fixed-time and any-time PAC Bayesian bounds in the batch learning setting. Performing causal forecast is a highlight of our methodology as its potential application to data with spatial and temporal short and long-range dependence. We then test the performance of our learning methodology by using linear predictors and data sets simulated from a spatio-temporal Ornstein-Uhlenbeck process. |
| title | Mixed moving average field guided learning for spatio-temporal data |
| topic | Machine Learning Statistics Theory 60E07, 60E15, 60G25, 60G60, 62C10 |
| url | https://arxiv.org/abs/2301.00736 |