Papers › On the Sample Complexity of Privately Learning Axis-Aligned Rectangles
On the Sample Complexity of Privately Learning Axis-Aligned Rectangles
Menachem Sadigurschi, Uri Stemmer
We revisit the fundamental problem of learning Axis-Aligned-Rectangles over a finite grid Xᵈ⊆ℝᵈ with differential privacy. Existing results show that the sample complexity of this problem is at most min{ d·log|X| , d^(1.5)·(log^*|X| )^(1.5)}. 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 Õ{d·(log^*|X|)^(1.5)}, 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.
Code
Repository list and official/mentioned flags are the archive's, frozen 2025-07-28. Reachability, where shown, is from one Syntology probe window (2026-09-16 to 2026-09-18); repositories not probed show nothing. GitHub stars are not tracked.
Code Syntology ran Syntology
Not run by Syntology. Nothing on this page verifies that the listed code works.
Results from the paper archive 2025-07-28
No leaderboard rows for this paper in the archive.
Report a problem or propose a change · a person checks every report against the paper or source before anything changes; decisions are listed on /corrections