Neural Negative Binomial Regression for Weekly Seismicity Forecasting: Per-Cell Dispersion Estimation and Tail Risk Assessment

2026-05-21 · Source: stat.ML updates on arXiv.org · Field: Technology & Digital — Artificial Intelligence & Machine Learning, Data Science & Analytics, Geospatial AI & Earth Systems Modeling · Depth: Expert, extended

Summary

The EarthquakeNet architecture introduces a Neural Negative Binomial Regression model for weekly seismicity forecasting in Central Asia, analyzing USGS catalog data from 2010–2024 for M≥3.0 events on a 3.0°×3.0° spatial grid. This model addresses the systematic violation of the Poisson equidispersion assumption, which a likelihood-ratio test rejected with p<10⁻¹⁷⁹. EarthquakeNet uniquely provides an endogenous per-cell estimate of the overdispersion parameter α via a neural network combining spatial embeddings and an MLP, without requiring explicit spatial covariance. Evaluated using a Walk-Forward protocol (2018–2023), the Hybrid DL NB model achieved an 8.6% reduction in Mean Poisson Deviance (MPD) compared to NB GLM. Crucially, it demonstrated a 12.5% lower Continuous Ranked Probability Score (CRPS) in the tail stratum (Y≥5), significantly improving extreme event risk assessment.

Key takeaway

For Machine Learning Engineers building earthquake forecasting models, particularly in tectonically active regions, you must move beyond Poisson assumptions. Your models will systematically underestimate extreme event risk if they ignore data overdispersion. Implement Negative Binomial regression with per-cell dispersion, like EarthquakeNet's approach, to accurately capture tail probabilities. Use the predicted distribution's quantiles to generate robust, uncertainty-aware alerts, ensuring your forecasts provide reliable risk assessment for critical natural hazard management.

Key insights

Seismic count data's overdispersion requires per-cell Negative Binomial modeling for accurate extreme event risk assessment.

Principles

• Seismic count data systematically violates Poisson equidispersion.
• Per-cell dispersion parameters improve extreme event tail risk assessment.
• Spatial embeddings capture latent geological heterogeneity without explicit covariance.

Method

EarthquakeNet employs spatial embeddings and an MLP to predict per-cell Negative Binomial parameters (μ, α) from physical features, optimized via NLL with softplus activation.

In practice

• Apply Negative Binomial regression for overdispersed count data.
• Utilize spatial embeddings to model unobserved regional characteristics.
• Generate risk-aware alerts using predicted distribution quantiles.

Topics

• Seismicity Forecasting
• Neural Negative Binomial Regression
• EarthquakeNet
• Overdispersion Modeling
• Spatial Embeddings
• Tail Risk Assessment

Code references

• Al1mkaYandere/seismic-probabilistic-modeling

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Editorial summary, takeaway, and curation by AIssential. Original article published by stat.ML updates on arXiv.org.