The space complexity of approximating the frequency moments
Journal of Computer and System Sciences
TAG: a Tiny AGgregation service for Ad-Hoc sensor networks
OSDI '02 Proceedings of the 5th symposium on Operating systems design and implementationCopyright restrictions prevent ACM from being able to make the PDFs for this conference available for downloading
Data streams: algorithms and applications
Foundations and Trends® in Theoretical Computer Science
Sketching in adversarial environments
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Interactive privacy via the median mechanism
Proceedings of the forty-second ACM symposium on Theory of computing
A Multiplicative Weights Mechanism for Privacy-Preserving Data Analysis
FOCS '10 Proceedings of the 2010 IEEE 51st Annual Symposium on Foundations of Computer Science
The Limits of Two-Party Differential Privacy
FOCS '10 Proceedings of the 2010 IEEE 51st Annual Symposium on Foundations of Computer Science
Algorithms for distributed functional monitoring
ACM Transactions on Algorithms (TALG)
On the Power of Adaptivity in Sparse Recovery
FOCS '11 Proceedings of the 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science
Analyzing graph structure via linear measurements
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Calibrating noise to sensitivity in private data analysis
TCC'06 Proceedings of the Third conference on Theory of Cryptography
Graph sketches: sparsification, spanners, and subgraphs
PODS '12 Proceedings of the 31st symposium on Principles of Database Systems
The Privacy of the Analyst and the Power of the State
FOCS '12 Proceedings of the 2012 IEEE 53rd Annual Symposium on Foundations of Computer Science
| Hi-index | 0.00 |
Linear sketches are powerful algorithmic tools that turn an n-dimensional input into a concise lower-dimensional representation via a linear transformation. Such sketches have seen a wide range of applications including norm estimation over data streams, compressed sensing, and distributed computing. In almost any realistic setting, however, a linear sketch faces the possibility that its inputs are correlated with previous evaluations of the sketch. Known techniques no longer guarantee the correctness of the output in the presence of such correlations. We therefore ask: Are linear sketches inherently non-robust to adaptively chosen inputs? We give a strong affirmative answer to this question. Specifically, we show that no linear sketch approximates the Euclidean norm of its input to within an arbitrary multiplicative approximation factor on a polynomial number of adaptively chosen inputs. The result remains true even if the dimension of the sketch is d=n-o(n) and the sketch is given unbounded computation time. Our result is based on an algorithm with running time polynomial in d that adaptively finds a distribution over inputs on which the sketch is incorrect with constant probability. Our result implies several corollaries for related problems including lp-norm estimation and compressed sensing. Notably, we resolve an open problem in compressed sensing regarding the feasibility of l2/l2-recovery guarantees in presence of computationally bounded adversaries.