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Dynamic Attention (DynAttn): Interpretable High-Dimensional Spatio-Temporal Forecasting (with Application to Conflict Fatalities)

Stefano M. Iacus, Haodong Qi, Marcello Carammia, Thomas Juneau

TL;DR

DynAttn addresses the challenge of forecasting conflict fatalities in sparse, bursty, and non-stationary spatio-temporal data by integrating rolling-window estimation, shared elastic-net feature gates, a weight-tied Transformer encoder, and a ZINB likelihood to produce calibrated multi-horizon forecasts and exceedance probabilities for $H=1$ to $12$ months. The model yields coherent predictions for expected counts $reve{y}_t=(1- ho_t) u_t$ and exceedance probabilities $ ext{Pr}(Y_{t+h}\ge au)$, while providing diagnostics via gates, ablation, and elasticity to interpret regional dynamics. Empirical results on global country-level and PRIO-grid-level data show DynAttn substantially outperforming DynENet, LSTM, Prophet, PatchTST, and VIEWS, with especially large gains in sparse grid settings. The framework reveals that high-frequency signals of recent violence and diffusion form the core predictive backbone, with climate stress acting variably as amplifier or driver across theaters, highlighting the value of a flexible, interpretable forecasting system for conflict analytics.

Abstract

Forecasting conflict-related fatalities remains a central challenge in political science and policy analysis due to the sparse, bursty, and highly non-stationary nature of violence data. We introduce DynAttn, an interpretable dynamic-attention forecasting framework for high-dimensional spatio-temporal count processes. DynAttn combines rolling-window estimation, shared elastic-net feature gating, a compact weight-tied self-attention encoder, and a zero-inflated negative binomial (ZINB) likelihood. This architecture produces calibrated multi-horizon forecasts of expected casualties and exceedance probabilities, while retaining transparent diagnostics through feature gates, ablation analysis, and elasticity measures. We evaluate DynAttn using global country-level and high-resolution PRIO-grid-level conflict data from the VIEWS forecasting system, benchmarking it against established statistical and machine-learning approaches, including DynENet, LSTM, Prophet, PatchTST, and the official VIEWS baseline. Across forecast horizons from one to twelve months, DynAttn consistently achieves substantially higher predictive accuracy, with particularly large gains in sparse grid-level settings where competing models often become unstable or degrade sharply. Beyond predictive performance, DynAttn enables structured interpretation of regional conflict dynamics. In our application, cross-regional analyses show that short-run conflict persistence and spatial diffusion form the core predictive backbone, while climate stress acts either as a conditional amplifier or a primary driver depending on the conflict theater.

Dynamic Attention (DynAttn): Interpretable High-Dimensional Spatio-Temporal Forecasting (with Application to Conflict Fatalities)

TL;DR

DynAttn addresses the challenge of forecasting conflict fatalities in sparse, bursty, and non-stationary spatio-temporal data by integrating rolling-window estimation, shared elastic-net feature gates, a weight-tied Transformer encoder, and a ZINB likelihood to produce calibrated multi-horizon forecasts and exceedance probabilities for to months. The model yields coherent predictions for expected counts and exceedance probabilities , while providing diagnostics via gates, ablation, and elasticity to interpret regional dynamics. Empirical results on global country-level and PRIO-grid-level data show DynAttn substantially outperforming DynENet, LSTM, Prophet, PatchTST, and VIEWS, with especially large gains in sparse grid settings. The framework reveals that high-frequency signals of recent violence and diffusion form the core predictive backbone, with climate stress acting variably as amplifier or driver across theaters, highlighting the value of a flexible, interpretable forecasting system for conflict analytics.

Abstract

Forecasting conflict-related fatalities remains a central challenge in political science and policy analysis due to the sparse, bursty, and highly non-stationary nature of violence data. We introduce DynAttn, an interpretable dynamic-attention forecasting framework for high-dimensional spatio-temporal count processes. DynAttn combines rolling-window estimation, shared elastic-net feature gating, a compact weight-tied self-attention encoder, and a zero-inflated negative binomial (ZINB) likelihood. This architecture produces calibrated multi-horizon forecasts of expected casualties and exceedance probabilities, while retaining transparent diagnostics through feature gates, ablation analysis, and elasticity measures. We evaluate DynAttn using global country-level and high-resolution PRIO-grid-level conflict data from the VIEWS forecasting system, benchmarking it against established statistical and machine-learning approaches, including DynENet, LSTM, Prophet, PatchTST, and the official VIEWS baseline. Across forecast horizons from one to twelve months, DynAttn consistently achieves substantially higher predictive accuracy, with particularly large gains in sparse grid-level settings where competing models often become unstable or degrade sharply. Beyond predictive performance, DynAttn enables structured interpretation of regional conflict dynamics. In our application, cross-regional analyses show that short-run conflict persistence and spatial diffusion form the core predictive backbone, while climate stress acts either as a conditional amplifier or a primary driver depending on the conflict theater.
Paper Structure (66 sections, 39 equations, 13 figures, 10 tables)

This paper contains 66 sections, 39 equations, 13 figures, 10 tables.

Table of Contents

  1. Introduction
  2. Nowcasting Conflict Intensity via DynAttnn
  3. Transformers for Time Series Analysis
  4. Comparison with Pre-Transformer Models
  5. Key Advantages of DynAttnn in Forecasting Conflict Intensity
  6. DynAttn Model description
  7. Windows, standardization, and gating.
  8. Transformer encoder and pooled representation.
  9. MLP heads and GELU activations.
  10. ZINB likelihood, expected counts, and exceedance probability.
  11. Loss function.
  12. Rolling optimization and region-specific models.
  13. Modeling Choices and Implementation
  14. Softplus gates for stable and interpretable feature selection.
  15. GELU in the encoder and heads vs. ReLU.
  16. ...and 51 more sections

Figures (13)

  • Figure 1: Architecture of the gated attention ZINB model.
  • Figure 2: Observed number of fatalities by country in testing period, August 2024 --July 2025. Darker colors indicate more conflict fatalities transformed by $\log(Y+1)$, and larger country labels indicate greater absolute number of fatalities. Given PRIO's country definition, the territory of Israel also contains Palestine.
  • Figure 3: Observed number of fatalities by grid in testing set, August 2024 --July 2025. Darker colors indicate more conflict fatalities transformed by $\log(Y+1)$.
  • Figure 4: Observed and predicted trends of fatalities. Observed values in circles and predicted values in lines.
  • Figure 5: Predicted risk of at least 25 fatalities in testing set, August 2024 --July 2025. Darker colors indicate higher probability of encountering conflict fatalities.
  • ...and 8 more figures