• Corpus ID: 237640652

Bounded Space Differentially Private Quantiles

@inproceedings{Alabi2021BoundedSD,
  title={Bounded Space Differentially Private Quantiles},
  author={Daniel Alabi and Omri Ben-Eliezer and Anamay Chaturvedi},
  year={2021}
}
Estimating the quantiles of a large dataset is a fundamental problem in both the streaming algorithms literature and the differential privacy literature. However, all existing private mechanisms for distribution-independent quantile computation require space at least linear in the input size n. In this work, we devise a differentially private algorithm for the quantile estimation problem, with strongly sublinear space complexity, in the one-shot and continual observation settings. Our basic… 

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References

SHOWING 1-10 OF 55 REFERENCES

Differentially Private Approximate Quantiles

TLDR
A simple recursive DP algorithm, which the authors call Approximate Quantiles (AQ), is described, which gives a worst case upper bound on its error, and shows that its error is much lower than of previous implementations on several different datasets.

Relative Error Streaming Quantiles

TLDR
This paper presents a randomized algorithm storing O(log1.5 (ε n)/ε) items, which is within an O(√log(ε n)) factor of optimal, rendering it suitable for parallel and distributed computing environments.

Optimal Quantile Approximation in Streams

TLDR
This paper resolves one of the longest standing basic problems in the streaming computational model and proves a qualitative gap between randomized and deterministic quantile sketching for which an Ω((1/ε)log log (1/δ)) lower bound is known.

Optimal Private Median Estimation under Minimal Distributional Assumptions

TLDR
This work studies the fundamental task of estimating the median of an underlying distribution from a finite number of samples, under pure differential privacy constraints, and designs a polynomial-time differentially private algorithm which provably achieves the optimal performance.

Differentially-Private Multi-Party Sketching for Large-Scale Statistics

TLDR
A scenario where multiple organizations holding large amounts of sensitive data from their users wish to compute aggregate statistics on this data while protecting the privacy of individual users is considered, and a general framework for constructing multi-party differentially private protocols for several other sketching algorithms is obtained.

Pan-private algorithms via statistics on sketches

TLDR
This work presents the first known lower bounds explicitly for pan privacy, stronger than those implied by differential privacy or dynamic data streaming alone and hold even if unbounded memory and/or unbounded processing time are allowed.

Differentially Private Histograms under Continual Observation: Streaming Selection into the Unknown

TLDR
A meta-algorithm is presented that can use existing one-shot top-k private algorithms as a subroutine to continuously release DP histograms from a stream and more practical DP algorithms for two settings: continuously releasing the top- k counts from a histogram over a known domain when an event can consist of an arbitrary number of items.

Differential Privacy on Finite Computers

TLDR
Strict polynomial-time discrete algorithms for approximate histograms whose simultaneous accuracy matches that of the Laplace Mechanism up to constant factors, while retaining the same (pure) differential privacy guarantee are provided.

A Tight Lower Bound for Comparison-Based Quantile Summaries

TLDR
This paper focuses on comparison-based quantile summaries that can only compare two items and are otherwise completely oblivious of the universe, and improves the lower bound for biased quantiles, which provide a stronger, relative-error guarantee of (1+-ε)⋅ φ, and for other related computational tasks.

Secure Sublinear Time Differentially Private Median Computation

TLDR
This paper presents an efficient secure computation of a differentially private median of the union of two large, confidential data sets via the exponential mechanism, which has a runtime sublinear in the size of the data universe and utility like the central model without a trusted third party.
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