2021
DOI: 10.48550/arxiv.2111.06578
|View full text |Cite
Preprint
|
Sign up to set email alerts
|

Differential privacy and robust statistics in high dimensions

Abstract: We introduce a universal framework for characterizing the statistical efficiency of a statistical estimation problem with differential privacy guarantees. Our framework, which we call High-dimensional Propose-Test-Release (HPTR), builds upon three crucial components: the exponential mechanism from [MT07], robust statistics, and the Propose-Test-Release mechanism from [DL09]. Gluing all these together is the concept of resilience, which is central to robust statistical estimation. Resilience guides the design o… Show more

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...
2
1
1
1

Citation Types

0
7
0

Year Published

2021
2021
2022
2022

Publication Types

Select...
3

Relationship

1
2

Authors

Journals

citations
Cited by 3 publications
(7 citation statements)
references
References 60 publications
0
7
0
Order By: Relevance
“…Assumption A.4 can be relaxed to heavy-tail bounds with bounded k-th moment on A i , in which case we expect the second term in Eq. ( 10) to scale as O(d( log(1/δ)/εn) 1−1/k ), drawing analogy from a similar trend in a computationally inefficient DP-PCA without spectral gap [56,Corollary 6.10]. When a fraction of data is corrupted, recent advances in [74,51,40] provide optimal algorithms for PCA.…”
Section: Discussionmentioning
confidence: 99%
See 3 more Smart Citations
“…Assumption A.4 can be relaxed to heavy-tail bounds with bounded k-th moment on A i , in which case we expect the second term in Eq. ( 10) to scale as O(d( log(1/δ)/εn) 1−1/k ), drawing analogy from a similar trend in a computationally inefficient DP-PCA without spectral gap [56,Corollary 6.10]. When a fraction of data is corrupted, recent advances in [74,51,40] provide optimal algorithms for PCA.…”
Section: Discussionmentioning
confidence: 99%
“…When a fraction of data is corrupted, recent advances in [74,51,40] provide optimal algorithms for PCA. However, existing approach of [56] for robust and private PCA is computationally intractable. Borrowing ideas from robust and private mean estimation in [55], one can design an efficient algorithm, but at the cost of sub-optimal sample complexity.…”
Section: Discussionmentioning
confidence: 99%
See 2 more Smart Citations
“…However, none of their results give computationally efficient estimators for pure DP. A simultaneous and independent work of [LKO21] demonstrates an interesting connection between resilience [SCV18] and private estimation. They exploit this connection to design robust and private algorithms for a variety of settings, including mean estimation, covariance estimation, PCA, and more.…”
Section: Robust Statistics and Privacymentioning
confidence: 99%