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## Complexity theoretic lower bounds for sparse principal component detection (2013)

Venue: | In COLT 2013 – The 26th Conference on Learning Theory |

Citations: | 31 - 3 self |

### Citations

7418 | Convex Optimization
- Boyd, Vandenberghe
- 2004
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Citation Context ...a semidefinite program in its canonical form with a polynomial number of constraints and can therefore be solved in polynomial time up to arbitrary precision using interior point methods for example (=-=Boyd and Vandenberghe, 2004-=-), as shown in Appendix A. Consider the following test ψd,n,k = 1{SDP(n)k (Σ̂) > 1 + τ} , τ > 0 , (7) where SDP (n) k is a 1/ √ n-approximation of SDPk. Bach et al. (2010) show that SDP (n) k can be c... |

273 | A direct formulation for sparse pca using semidefinite programming. - d’Aspremont, Ghaoui, et al. - 2007 |

234 | Uniform central limit theorems - Dudley - 1999 |

130 | Finding a large hidden clique in a random graph. Random Structures and Algorithms - Alon, Krivelevich, et al. - 1999 |

110 | Eigenvalues and graph bisection: An average-case analysis - Boppana - 1987 |

107 | On consistency and sparsity for principal components analysis in high dimensions. - Johnstone, Lu - 2009 |

85 | High-dimensional analysis of semidefinite programming relaxations for sparse principal component analysis - Amini, Wainwright |

84 | Finite exchangeable sequences - Diaconis, Freedman - 1980 |

65 | Finding and certifying a large hidden clique in a semirandom graph. Random Structures and Algorithms - Feige, Krauthgamer - 2000 |

49 | Nuclear norm minimization for the planted clique and biclique problems. Under review - Ames, Vavasis - 2009 |

46 | Expected complexity of graph partitioning problems. - Kucera - 1995 |

45 | Computational and statistical tradeoffs via convex relaxation. - Chandrasekaran, Jordan - 2013 |

42 | Optimal detection of sparse principal components in high dimension. Available online at http://arXiv.org/abs/1202.5070, - Berthet, Rigollet - 2012 |

41 | Clique is Hard to Approximate Within n1−ǫ. - Hastad - 1996 |

38 | On combinatorial testing problems - Addario-Berry, Broutin, et al. - 2010 |

38 | Hiding cliques for cryptographic security. - Juels, Peinado - 2000 |

34 | Large cliques elude the metropolis process. - Jerrum - 1992 |

31 | How hard is it to approximate the best Nash equilibrium? - Hazan, Krauthgamer - 2011 |

30 | Detection of an anomalous cluster in a network. - Arias-Castro, Candès, et al. - 2011 |

28 | Approximating the independence number and the chromatic number in expected polynomial time - Krivelevich, Vu |

27 | The probable value of the Lovász–Schrijver relaxations for maximum independent set - Feige, Krauthgamer - 2003 |

21 | Detection of a sparse submatrix of a high-dimensional noisy matrix. Available online http://arxiv.org/abs/1109.0898,
- Butucea, Ingster
- 2011
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Citation Context ... of the form signal-plus-noise, where the signal is a vector with combinatorial structure (Addario-Berry et al., 2010; Arias-Castro et al., 2011a,b; Arias-Castro and Verzelen, 2013) or even a matrix (=-=Butucea and Ingster, 2013-=-; Sun and Nobel, 2013; Kolar et al., 2011; Balakrishnan et al., 2011). The matrix detection problem was pushed beyond the signalplus-noise model towards more complicated dependence structures in Arias... |

21 | Finding hidden cliques in linear time with high probability. arXiv preprint arXiv:1010.2997, - Dekel, Gurel-Gurevich, et al. - 2010 |

13 | Ronitt Rubinfeld, and Ning Xie. Testing k-wise and almost k-wise independence - Alon, Andoni, et al. - 2007 |

13 | Minimax localization of structural information in large noisy matrices.
- Kolar, Balakrishnan, et al.
- 2011
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Citation Context ... is a vector with combinatorial structure (Addario-Berry et al., 2010; Arias-Castro et al., 2011a,b; Arias-Castro and Verzelen, 2013) or even a matrix (Butucea and Ingster, 2013; Sun and Nobel, 2013; =-=Kolar et al., 2011-=-; Balakrishnan et al., 2011). The matrix detection problem was pushed beyond the signalplus-noise model towards more complicated dependence structures in Arias-Castro et al. (2012, 2013); Berthet and ... |

9 | Detecting positive correlations in a multivariate sample. arXiv preprint arXiv:1202.5536, - Castro, Bubeck, et al. - 2012 |

9 |
Statistical algorithms and a lower bound for planted clique
- Feldman, Grigorescu, et al.
- 2013
(Show Context)
Citation Context ...ollet Note that we do not specify a computational model intentionally. Indeed, for some restricted computational models, Hypothesis APC can be proved to be true for all a < b ∈ (0, 1) (Rossman, 2010; =-=Feldman et al., 2013-=-). Moreover, for more powerful computational models such as Turing machines, this hypothesis is conjectured to be true. It was shown in Berthet and Rigollet (2012) that improving the detection level o... |

6 | Sebastien Bubeck, and Gabor Lugosi. Detecting Positive Correlations in a Multivariate Sample. - Arias-Castro - 2015 |

5 | Sparse principal component analysis and iterative - Ma - 2013 |

4 | Ghaoui, Approximation bounds for sparse principal component analysis, ArXiv:1205.0121 - d’Aspremont, Bach, et al. - 2012 |

3 | Zongming Ma, and Yihong Wu, Sparse PCA: Optimal rates and adaptive estimation, Arxiv Preprint - Cai - 2012 |

2 | Damla Ahipasaoglu, and Alexandre d’Aspremont, Convex relaxations for subset selection, Arxiv Preprint - Bach, Selin - 2010 |

1 | On the inapproximability of the densest κ-subgraph problem. Unpublished - Alon, Arora, et al. - 2011 |