Conceptα=ν匹配

Tail Index Matching

A mechanism in stable generative models that makes the power-law tail index α of the generated distribution equal to the tail index ν of the target distribution. It is a necessary condition for correctly extrapolating extreme quantiles.

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Oct 15

For a target distribution with tail index ν, the stable generative model can asymptotically correctly reproduce the scaling behavior of extreme quantiles if and only if α=ν.

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Unverified

For a target distribution with tail index ν, the stable generative model can asymptotically correctly reproduce the scaling behavior of extreme quantiles if and only if α=ν.

50%

Source Articles

α-Stable Score-Based Generative Models: A Theoretical Breakthrough from Global to Tail ConvergenceOct 15