An Extreme Value Perspective on Learning Stress Laws

• URL: http://arxiv.org/abs/2607.10700v1
• Date: Sun, 12 Jul 2026 10:46:41 GMT
• Title: An Extreme Value Perspective on Learning Stress Laws
• Abstract summary: We introduce Self-Similar Generative Estimation (SS-GEN), a method for simulating rare-event probabilities in both heavy and light-tailed settings.<n>SS-GEN exploits tail structure to decompose the tail distribution into an explicit radial component and a non-parametric angular component.<n>The resulting sampler generates representative extreme scenarios and supports probability estimation far beyond the observed data.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We introduce Self-Similar Generative Estimation (SS-GEN), a method for simulating multivariate tail events and estimating rare-event probabilities in both heavy and light-tailed settings. SS-GEN exploits asymptotic tail structure to decompose the tail distribution into an explicit radial component and a nonparametric angular component, reducing tail learning to a compact-domain problem that can be handled by off-the-shelf deep generative models. The resulting sampler generates representative extreme scenarios and supports probability estimation far beyond the observed data. Under mild nonparametric tail assumptions, we show that the SS-GEN density is asymptotically exact in the tail, with vanishing uniform relative error for regularly varying distributions and vanishing uniform log-relative error for Weibull-type distributions. Unlike existing approaches that rely on specialized architectures or parametric tail specifications, SS-GEN leverages asymptotic tail structure to enable standard generative models to generate representative extreme samples and estimate rare-event probabilities beyond the observed data.

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