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- W3213641381 abstract "We revisit the fundamental problem of learning Axis-Aligned-Rectangles over a finite grid $X^dsubseteq{mathbb{R}}^d$ with differential privacy. Existing results show that the sample complexity of this problem is at most $minleft{ d{cdot}log|X| ;,; d^{1.5}{cdot}left(log^*|X| right)^{1.5}right}$. That is, existing constructions either require sample complexity that grows linearly with $log|X|$, or else it grows super linearly with the dimension $d$. We present a novel algorithm that reduces the sample complexity to only $tilde{O}left{d{cdot}left(log^*|X|right)^{1.5}right}$, attaining a dimensionality optimal dependency without requiring the sample complexity to grow with $log|X|$.The technique used in order to attain this improvement involves the deletion of exposed data-points on the go, in a fashion designed to avoid the cost of the adaptive composition theorems. The core of this technique may be of individual interest, introducing a new method for constructing statistically-efficient private algorithms." @default.
- W3213641381 created "2021-11-22" @default.
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- W3213641381 date "2021-12-06" @default.
- W3213641381 modified "2023-09-24" @default.
- W3213641381 title "On the Sample Complexity of Privately Learning Axis-Aligned Rectangles" @default.
- W3213641381 hasPublicationYear "2021" @default.
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