Fuk-Nagaev Inequality
The Fuk-Nagaev inequality is a concentration inequality for handling heavy-tailed random variables. It provides looser tail probability bounds than traditional inequalities and is applicable when the noise variance is infinite or only finite moments are available.
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The paper adopts a recently developed Hilbert-valued Fuk-Nagaev inequality, extending the concentration analysis from the scalar case to function spaces.
The study uses the Hilbert-valued Fuk-Nagaev inequality to establish, under only finite weak moment conditions (rather than exponential moment conditions), the same minimax optimal rate as under light-tailed noise.
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The paper adopts a recently developed Hilbert-valued Fuk-Nagaev inequality, extending the concentration analysis from the scalar case to function spaces.
50%UnverifiedThe study uses the Hilbert-valued Fuk-Nagaev inequality to establish, under only finite weak moment conditions (rather than exponential moment conditions), the same minimax optimal rate as under light-tailed noise.
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