Derives explicit minimax quantile lower bounds for Gaussian mean estimation and K-armed bandits under interactive decision making and MI privacy, with log(1/δ)/n and √(KT log(1/δ)) scalings.
Distance-based and continuum Fano inequalities with applications to statistical estimation
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abstract
In this technical note, we give two extensions of the classical Fano inequality in information theory. The first extends Fano's inequality to the setting of estimation, providing lower bounds on the probability that an estimator of a discrete quantity is within some distance $t$ of the quantity. The second inequality extends our bound to a continuum setting and provides a volume-based bound. We illustrate how these inequalities lead to direct and simple proofs of several statistical minimax lower bounds.
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cs.LG 1years
2026 1verdicts
UNVERDICTED 1representative citing papers
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Minimax Quantile Lower Bounds for Interactive Statistical Decision Making with Privacy
Derives explicit minimax quantile lower bounds for Gaussian mean estimation and K-armed bandits under interactive decision making and MI privacy, with log(1/δ)/n and √(KT log(1/δ)) scalings.