Manifold Constrained Conformal Prediction for Spatial Events

2026-02-23 · Source: stat.ML updates on arXiv.org · Field: Science & Research — Environmental Science & Earth Systems, Mathematics & Computational Sciences, Artificial Intelligence & Machine Learning · Depth: Expert, extended

Summary

Manifold Constrained Conformal Prediction (MCCP) is a novel method for constructing calibrated prediction sets for spatial event clouds, such as tropical cyclone genesis and earthquake locations. Addressing the challenge of uncertainty quantification for natural hazards, which involve discrete, variable-cardinality spatial configurations, MCCP represents point clouds as empirical measures. It scores these using spherical sliced Wasserstein distance (SSW) and constrains the resulting distribution-valued prediction sets to align with the training data manifold. The method includes a modified flow-based sampling procedure to generate calibrated ensembles. Numerical experiments on synthetic data, tropical cyclone genesis, and California earthquake occurrences demonstrate MCCP's effectiveness, achieving near-nominal coverage. It consistently shows significantly lower energy distance and manifold distance compared to highest predictive density region (HDR) and generative model baselines, with an ED of 2.39 for tropical cyclones and 0.47 for earthquakes.

Key takeaway

For Machine Learning Engineers developing spatial event forecasting systems, if your models predict discrete, variable-cardinality events like natural hazards, you should consider Manifold Constrained Conformal Prediction. This method provides calibrated uncertainty sets with coverage guarantees, ensuring predictions are both statistically sound and physically plausible. Adopting this approach can significantly improve the reliability and interpretability of your forecasts, crucial for accurate risk assessment in critical applications.

Key insights

Manifold-constrained conformal prediction uses Wasserstein distance and data manifold proximity to generate calibrated, physically plausible spatial event forecasts.

Principles

• Empirical measures enable optimal transport comparison for point clouds.
• Manifold constraints enhance physical realism of prediction sets.
• Constrained gradient flows sample complex prediction set boundaries.

Method

Represent point clouds as empirical measures, score with SSW distance, approximate data manifold, then use a constrained gradient flow to sample prediction set boundaries as ensembles.

In practice

• Forecast tropical cyclone genesis and earthquake locations.
• Utilize SSW distance for variable-cardinality spatial event comparison.
• Set manifold tolerance (ε) to cover all training data for coverage.

Topics

• Conformal Prediction
• Spatial Event Forecasting
• Wasserstein Distance
• Uncertainty Quantification
• Natural Hazards
• Manifold Learning

Best for: AI Scientist, Research Scientist, Machine Learning Engineer

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