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Deep Generative Spatiotemporal Engression for Probabilistic Forecasting of Epidemics

Rajdeep Pathak, Tanujit Chakraborty

TL;DR

Deep spatiotemporal engression methods to generate accurate and reliable probabilistic forecasts on low-frequency epidemic datasets are presented and the explainability of the proposal is explored to enhance the models'practical application for informed, timely public health interventions.

Abstract

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.

Deep Generative Spatiotemporal Engression for Probabilistic Forecasting of Epidemics

TL;DR

Deep spatiotemporal engression methods to generate accurate and reliable probabilistic forecasts on low-frequency epidemic datasets are presented and the explainability of the proposal is explored to enhance the models'practical application for informed, timely public health interventions.

Abstract

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.
Paper Structure (33 sections, 4 theorems, 32 equations, 18 figures, 13 tables, 4 algorithms)

This paper contains 33 sections, 4 theorems, 32 equations, 18 figures, 13 tables, 4 algorithms.

Table of Contents

  1. Introduction
  2. Motivating Example
  3. Background
  4. Proposed Methodology
  5. Graph Convolutional Engression Network
  6. Spatio-Temporal Engression Network
  7. Multivariate Engression Network
  8. Optimization
  9. Geometric Ergodicity and Asymptotic Stationarity
  10. Theoretical Results
  11. Practical Implications of Theoretical Results
  12. Simulation Study
  13. Application to Real-World Epidemic Datasets
  14. Datasets
  15. Spatial Autocorrelation
  16. ...and 18 more sections

Key Result

Theorem 1

Suppose that Assumptions (A1)-(A3) hold. If there exist real numbers $a \in (0,1)$ and $b$ such that $\|\mathcal{F}(z)\| \leq a \|z\| + b$, then the pre-additive recurrent network process defined in eq:recurrent_network_process is geometrically ergodic.

Figures (18)

  • Figure 1: (A) Lag plot $y_t$ vs. $y_{t-1}$ for weekly dengue data observed in Guainia, Colombia, and (B) ARIMA(1,0,0), ARNN, LSTM, and proposed MVEN (and a generated probabilistic cloud based on the proposal) fits on the data.
  • Figure 2: Simulation results for GCEN: empirical verification of (marginal) asymptotic stationarity and geometric ergodicity of the GCEN process through simulations for 500 time steps and 200 trials.
  • Figure 3: Geographical maps of the countries under study: (A) Japan, (B) China, (C) USA, (D) Belgium, (E) Colombia, and (F) Hungary - illustrating the mean incidence cases at each labeled node (see Tables \ref{['table:Japan_Characteristics']}-\ref{['table:Hungary_Characteristics']} in Appendix \ref{['appendix:global_properties']} for the corresponding node names). The territorial boundaries of the countries are shown for illustrative purposes only, without implying any political assertions.
  • Figure 4: Temporal evolution of global spatial autocorrelation (Moran’s I) across the six epidemiological datasets.
  • Figure 5: Schematic of the training, validation, and test set splits across various forecast evaluation windows.
  • ...and 13 more figures

Theorems & Definitions (11)

  • Remark 1
  • Definition 1: Irreducibility
  • Definition 2: Geometric ergodicity
  • Theorem 1
  • Theorem 2
  • Corollary 1: Asymptotic stationarity
  • Remark 2
  • Corollary 2
  • Remark 3
  • proof
  • ...and 1 more