Revealing information while preserving privacy
Proceedings of the twenty-second ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Practical privacy: the SuLQ framework
Proceedings of the twenty-fourth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Mechanism Design via Differential Privacy
FOCS '07 Proceedings of the 48th Annual IEEE Symposium on Foundations of Computer Science
Robust De-anonymization of Large Sparse Datasets
SP '08 Proceedings of the 2008 IEEE Symposium on Security and Privacy
Exact Matrix Completion via Convex Optimization
Foundations of Computational Mathematics
The power of convex relaxation: near-optimal matrix completion
IEEE Transactions on Information Theory
Boosting and Differential Privacy
FOCS '10 Proceedings of the 2010 IEEE 51st Annual Symposium on Foundations of Computer Science
A Multiplicative Weights Mechanism for Privacy-Preserving Data Analysis
FOCS '10 Proceedings of the 2010 IEEE 51st Annual Symposium on Foundations of Computer Science
Beating randomized response on incoherent matrices
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
Iterative constructions and private data release
TCC'12 Proceedings of the 9th international conference on Theory of Cryptography
A near-optimal algorithm for differentially-private principal components
The Journal of Machine Learning Research
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We consider differentially private approximate singular vector computation. Known worst-case lower bounds show that the error of any differentially private algorithm must scale polynomially with the dimension of the singular vector. We are able to replace this dependence on the dimension by a natural parameter known as the coherence of the matrix that is often observed to be significantly smaller than the dimension both theoretically and empirically. We also prove a matching lower bound showing that our guarantee is nearly optimal for every setting of the coherence parameter. Notably, we achieve our bounds by giving a robust analysis of the well-known power iteration algorithm, which may be of independent interest. Our algorithm also leads to improvements in worst-case settings and to better low-rank approximations in the spectral norm.