# Deep Generative Spatiotemporal Engression for Probabilistic Forecasting of Epidemics

arXiv: https://arxiv.org/abs/2603.07108 · HTML: https://mlsanity.com/paper/2603.07108/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 73 references that are in the map.
- First posted on arXiv 7 Mar 2026.

## Builds on (most cited first, 28 of 28)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Optuna: A Next-generation Hyperparameter Optimization Framework](https://mlsanity.com/paper/1907.10902/) (2019)
- [An Empirical Evaluation of Generic Convolutional and Recurrent Networks for Sequence Modeling](https://mlsanity.com/paper/1803.01271/) (2018)
- [Spatio-Temporal Graph Convolutional Networks: A Deep Learning Framework for Traffic Forecasting](https://mlsanity.com/paper/1709.04875/) (2017)
- [DeepAR: Probabilistic Forecasting with Autoregressive Recurrent Networks](https://mlsanity.com/paper/1704.04110/) (2017)
- [iTransformer: Inverted Transformers Are Effective for Time Series Forecasting](https://mlsanity.com/paper/2310.06625/) (2023)
- [N-BEATS: Neural basis expansion analysis for interpretable time series forecasting](https://mlsanity.com/paper/1905.10437/) (2019)
- [PyTorch Geometric Temporal: Spatiotemporal Signal Processing with Neural Machine Learning Models](https://mlsanity.com/paper/2104.07788/) (2021)
- [Deep Learning for Time Series Forecasting: Tutorial and Literature Survey](https://mlsanity.com/paper/2004.10240/) (2020)
- [Darts: User-Friendly Modern Machine Learning for Time Series](https://mlsanity.com/paper/2110.03224/) (2021)
- [DiffSTG: Probabilistic Spatio-Temporal Graph Forecasting with Denoising Diffusion Models](https://mlsanity.com/paper/2301.13629/) (2023)
- [Engression: Extrapolation through the Lens of Distributional Regression](https://mlsanity.com/paper/2307.00835/) (2023)
- [Do RNN and LSTM have Long Memory?](https://mlsanity.com/paper/2006.03860/) (2020)
- [Exploring Interpretable LSTM Neural Networks over Multi-Variable Data](https://mlsanity.com/paper/1905.12034/) (2019)
- [A Review of Graph Neural Networks in Epidemic Modeling](https://mlsanity.com/paper/2403.19852/) (2024)
- [Ensemble Conformalized Quantile Regression for Probabilistic Time Series Forecasting](https://mlsanity.com/paper/2202.08756/) (2022)
- [Permutation and Grouping Methods for Sharpening Gaussian Process Approximations](https://mlsanity.com/paper/1609.05372/) (2016)
- [Chickenpox Cases in Hungary: a Benchmark Dataset for Spatiotemporal Signal Processing with Graph Neural Networks](https://mlsanity.com/paper/2102.08100/) (2021)
- [EpiGNN: Exploring Spatial Transmission with Graph Neural Network for Regional Epidemic Forecasting](https://mlsanity.com/paper/2208.11517/) (2022)
- [Epicasting: An Ensemble Wavelet Neural Network (EWNet) for Forecasting Epidemics](https://mlsanity.com/paper/2206.10696/) (2022)
- [Deep Distributional Time Series Models and the Probabilistic Forecasting of Intraday Electricity Prices](https://mlsanity.com/paper/2010.01844/) (2020)
- [MSGNN: Multi-scale Spatio-temporal Graph Neural Network for Epidemic Forecasting](https://mlsanity.com/paper/2308.15840/) (2023)
- [A Study on Graph-Structured Recurrent Neural Networks and Sparsification with Application to Epidemic Forecasting](https://mlsanity.com/paper/1902.05113/) (2019)
- [Epidemic-guided deep learning for spatiotemporal forecasting of Tuberculosis outbreak](https://mlsanity.com/paper/2502.10786/) (2025)
- [Recalibrating probabilistic forecasts of epidemics](https://mlsanity.com/paper/2112.06305/) (2021)
- [E-STGCN: Extreme Spatiotemporal Graph Convolutional Networks for Air Quality Forecasting](https://mlsanity.com/paper/2411.12258/) (2024)

## Built on by (most cited first, 4 of 4)

- [Deep Generative Transformers for Probabilistic Time Series and Spatiotemporal Forecasting](https://mlsanity.com/paper/2603.11909/) (2026)
- [GraphSVR: A Graph Convolutional Support Vector Regression Framework for Robust Spatiotemporal Air Pollution Forecasting](https://mlsanity.com/paper/2605.03795/) (2026)
- [Long-Memory Reservoir Computing for Data-Scarce Dengue Forecasting](https://mlsanity.com/paper/2607.11272/) (2026)
- [Generalized Engression Models](https://mlsanity.com/paper/2610.01823/) (2026)

## Abstract (arXiv)

Accurate and reliable forecasting of epidemic incidences is critical for public health preparedness, yet it remains a challenging task due to complex nonlinear temporal dependencies and heterogeneous spatial interactions. Often, point forecasts generated by spatiotemporal models are unreliable in assigning uncertainty to future epidemic events. Probabilistic forecasting of epidemics is therefore crucial for providing the best or worst-case scenarios rather than a simple, often inaccurate, point estimate. We present deep spatiotemporal engression methods to generate accurate and reliable probabilistic forecasts on low-frequency epidemic datasets. The proposed methods act as distributional lenses, and out-of-sample probabilistic forecasts are generated by sampling from the trained models. Our frameworks encapsulate lightweight deep generative architectures, wherein uncertainty is quantified endogenously, driven by a pre-additive noise component during model construction. We establish geometric ergodicity and asymptotic stationarity of the spatiotemporal engression processes under mild assumptions on the network weights and pre-additive noise process. Comprehensive evaluations across six epidemiological datasets over three forecast horizons demonstrate that the proposal consistently outperforms several temporal and spatiotemporal benchmarks in both point and probabilistic forecasting. Additionally, we explore the explainability of the proposal to enhance the models' practical application for informed, timely public health interventions.