Mixed moving average field guided learning for spatio-temporal data

Imma Valentina Curato; Orkun Furat; Lorenzo Proietti; Bennet Stroeh

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arXiv · 2301.00736

Mixed moving average field guided learning for spatio-temporal data

Imma Valentina Curato·Orkun Furat·Lorenzo Proietti·Bennet Stroeh

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Abstract

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.

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BibTeX RIS

Imma Valentina Curato, Orkun Furat, Lorenzo Proietti, Bennet Stroeh. 2023-01-02. Mixed moving average field guided learning for spatio-temporal data. https://arxiv.org/abs/2301.00736

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