Self-Normalized Bernstein Inequality
A concentration inequality combining self-normalization with the advantages of the Bernstein bound, using the empirical variance as a normalizing factor so that no prior variance upper bound is required. It is robust to heteroscedasticity and heavy-tailed data and is suited to dependent-data settings.
Timeline (last 90 days)
The paper proposes a self-normalized Bernstein inequality for regenerative processes, providing new generalization error bounds for dependent data.
The inequality uses only the observed cycle lengths and explicitly retains the truncation term and the effect of the cycle after the observation period ends.
By selecting tuning parameters from a finite deterministic set, all but one term in the resulting bound are empirically computable, and the remaining term is related to the tail of the regeneration times.
The remaining term is related to the tail of the regeneration times, and in many cases of interest it is second-order and negligible in practice.
All Facts (4)
The paper proposes a self-normalized Bernstein inequality for regenerative processes, providing new generalization error bounds for dependent data.
50%UnverifiedThe inequality uses only the observed cycle lengths and explicitly retains the truncation term and the effect of the cycle after the observation period ends.
50%UnverifiedBy selecting tuning parameters from a finite deterministic set, all but one term in the resulting bound are empirically computable, and the remaining term is related to the tail of the regeneration times.
50%UnverifiedThe remaining term is related to the tail of the regeneration times, and in many cases of interest it is second-order and negligible in practice.
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