# Mixed moving average field guided learning for spatio-temporal data

arXiv: https://arxiv.org/abs/2301.00736 · HTML: https://mlsanity.com/paper/2301.00736/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 72 references that are in the map.
- First posted on arXiv 2 Jan 2023.

## Builds on (most cited first, 19 of 19)

- [Computing Nonvacuous Generalization Bounds for Deep (Stochastic) Neural Networks with Many More Parameters than Training Data](https://mlsanity.com/paper/1703.11008/) (2017)
- [Lipschitz regularity of deep neural networks: analysis and efficient estimation](https://mlsanity.com/paper/1805.10965/) (2018)
- [Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equations](https://mlsanity.com/paper/1711.10561/) (2017)
- [Efficient and Accurate Estimation of Lipschitz Constants for Deep Neural Networks](https://mlsanity.com/paper/1906.04893/) (2019)
- [User-friendly introduction to PAC-Bayes bounds](https://mlsanity.com/paper/2110.11216/) (2021)
- [Deep Learning for Precipitation Nowcasting: A Benchmark and A New Model](https://mlsanity.com/paper/1706.03458/) (2017)
- [Theory-guided Data Science: A New Paradigm for Scientific Discovery from Data](https://mlsanity.com/paper/1612.08544/) (2016)
- [A Primer on PAC-Bayesian Learning](https://mlsanity.com/paper/1901.05353/) (2019)
- [A Strongly Quasiconvex PAC-Bayesian Bound](https://mlsanity.com/paper/1608.05610/) (2016)
- [Simpler PAC-Bayesian Bounds for Hostile Data](https://mlsanity.com/paper/1610.07193/) (2016)
- [Fast Rates for General Unbounded Loss Functions: from ERM to Generalized Bayes](https://mlsanity.com/paper/1605.00252/) (2016)
- [Machine Learning for Spatiotemporal Sequence Forecasting: A Survey](https://mlsanity.com/paper/1808.06865/) (2018)
- [PAC-Bayes under potentially heavy tails](https://mlsanity.com/paper/1905.07900/) (2019)
- [DisCo: Physics-Based Unsupervised Discovery of Coherent Structures in Spatiotemporal Systems](https://mlsanity.com/paper/1909.11822/) (2019)
- [Spatio-temporal Ornstein-Uhlenbeck processes: theory, simulation and statistical inference](https://mlsanity.com/paper/1504.08327/) (2015)
- [Causal Future Prediction in a Minkowski Space-Time](https://mlsanity.com/paper/2008.09154/) (2020)
- [Bridging between short-range and long-range dependence with mixed spatio-temporal Ornstein-Uhlenbeck processes](https://mlsanity.com/paper/1704.04070/) (2017)
- [Inference and forecasting for continuous-time integer-valued trawl processes](https://mlsanity.com/paper/2107.03674/) (2021)
- [The LICORS Cabinet: Nonparametric Algorithms for Spatio-temporal Prediction](https://mlsanity.com/paper/1506.02686/) (2015)

## Built on by (most cited first, 1 of 1)

- [Spatio-temporal probabilistic forecast using MMAF-guided learning](https://mlsanity.com/paper/2603.15055/) (2026)

## Abstract (arXiv)

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.