Theoretical guarantees for neural likelihood-free estimators in spatial extremes

Establish theoretical accuracy guarantees for neural likelihood-free parameter estimation methods used in extreme-value applications, specifically characterizing how estimation error depends on the chosen neural network architecture and the number of training samples when modeling spatial or spatio-temporal extremes.

Background

The paper highlights growing interest in neural, likelihood-free inference methods (e.g., neural Bayes estimators) to overcome computational hurdles in spatial extreme-value models where likelihoods are expensive or intractable. While these amortized approaches can provide rapid parameter estimates after training, the authors note that formal theoretical guarantees are lacking.

In particular, the relationship between estimator accuracy, neural network architecture, and training data size remains unspecified for extreme-value applications. Formalizing these guarantees would underpin the reliability of neural estimators when extrapolating to rare-event regimes central to environmental risk assessment.

References

For example, theoretical guarantees on the accuracy of neural estimators in terms of the chosen NN architecture and number of training samples remain to be established.

— Modeling of spatial extremes in environmental data science: Time to move away from max-stable processes  (2401.17430 - Huser et al., 2024) in Section 4 (Conclusion)

This is a scaling property ($N$-independence), not a practicality statement: the prescribed capacity grows with a steep $\epsilon$-exponent---reflecting the flatness of the quadratic enclosure at the origin (Remark~\ref{rem:design})---and whether the experimental widths satisfy it is not established.

— Scalable Minimum-Volume Simplex Estimation with Non-asymptotic Analysis  (2609.25576 - Li et al., 22 Sep 2026) in Section 2, Proposition 4 discussion: Approximation rate of the coordinate network