Communications of the ACM
Weakly learning DNF and characterizing statistical query learning using Fourier analysis
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
Expected complexity of graph partitioning problems
Discrete Applied Mathematics - Special issue: Combinatorial Optimization 1992 (CO92)
Efficient noise-tolerant learning from statistical queries
Journal of the ACM (JACM)
Finding a large hidden clique in a random graph
Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
Computational sample complexity and attribute-efficient learning
Journal of Computer and System Sciences
Finding and certifying a large hidden clique in a semirandom graph
Random Structures & Algorithms
Hiding Cliques for Cryptographic Security
Designs, Codes and Cryptography
Some optimal inapproximability results
Journal of the ACM (JACM)
The Probable Value of the Lovász-Schrijver Relaxations for Maximum Independent Set
SIAM Journal on Computing
On Learning Correlated Boolean Functions Using Statistical Queries
ALT '01 Proceedings of the 12th International Conference on Algorithmic Learning Theory
On the Efficiency of Noise-Tolerant PAC Algorithms Derived from Statistical Queries
Annals of Mathematics and Artificial Intelligence
Relations between Average Case Complexity and Approximation Complexity
CCC '02 Proceedings of the 17th IEEE Annual Conference on Computational Complexity
Spectral Partitioning of Random Graphs
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Ruling Out PTAS for Graph Min-Bisection, Densest Subgraph and Bipartite Clique
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Practical privacy: the SuLQ framework
Proceedings of the twenty-fourth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
New lower bounds for statistical query learning
Journal of Computer and System Sciences - Special issue on COLT 2002
Testing k-wise and almost k-wise independence
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
A simple polynomial-time rescaling algorithm for solving linear programs
Mathematical Programming: Series A and B
Probabilistic computations: Toward a unified measure of complexity
SFCS '77 Proceedings of the 18th Annual Symposium on Foundations of Computer Science
An Efficient Rescaled Perceptron Algorithm for Conic Systems
Mathematics of Operations Research
Random Tensors and Planted Cliques
APPROX '09 / RANDOM '09 Proceedings of the 12th International Workshop and 13th International Workshop on Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques
Small Clique Detection and Approximate Nash Equilibria
APPROX '09 / RANDOM '09 Proceedings of the 12th International Workshop and 13th International Workshop on Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques
Graph partitioning via adaptive spectral techniques
Combinatorics, Probability and Computing
Public-key cryptography from different assumptions
Proceedings of the forty-second ACM symposium on Theory of computing
Detecting high log-densities: an O(n¼) approximation for densest k-subgraph
Proceedings of the forty-second ACM symposium on Theory of computing
Characterizing statistical query learning: simplified notions and proofs
ALT'09 Proceedings of the 20th international conference on Algorithmic learning theory
How Hard Is It to Approximate the Best Nash Equilibrium?
SIAM Journal on Computing
Polynomial integrality gaps for strong SDP relaxations of Densest k-subgraph
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Nuclear norm minimization for the planted clique and biclique problems
Mathematical Programming: Series A and B - Special Issue on Cone Programming and its Applications
A complete characterization of statistical query learning with applications to evolvability
Journal of Computer and System Sciences
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We introduce a framework for proving lower bounds on computational problems over distributions, based on a class of algorithms called statistical algorithms. For such algorithms, access to the input distribution is limited to obtaining an estimate of the expectation of any given function on a sample drawn randomly from the input distribution, rather than directly accessing samples. Most natural algorithms of interest in theory and in practice, e.g., moments-based methods, local search, standard iterative methods for convex optimization, MCMC and simulated annealing, are statistical algorithms or have statistical counterparts. Our framework is inspired by and generalize the statistical query model in learning theory [34]. Our main application is a nearly optimal lower bound on the complexity of any statistical algorithm for detecting planted bipartite clique distributions (or planted dense subgraph distributions) when the planted clique has size O(n1/2-δ) for any constant δ 0. Variants of these problems have been assumed to be hard to prove hardness for other problems and for cryptographic applications. Our lower bounds provide concrete evidence of hardness, thus supporting these assumptions.