#### DMCA

## Convex Relaxations for Subset Selection (2010)

Citations: | 3 - 0 self |

### Citations

7508 |
Matrix Analysis
- Horn, Johnson
- 1985
(Show Context)
Citation Context ...e matrices A. Proposition 2 Let A ∈ Sp, with A ≽ 0 and k > 0 and suppose diag(A) ≥ 0. We have where λ k max(A) is the optimal value of problem (4). k p λmax(A) ≤ λ k max(A) ≤ λmax(A) (7) Proof. From (=-=Horn and Johnson, 1985-=-, §4.3.14), when A ≽ 0, we have λ i max (A) ≥ i i + 1 λi+1 max (A) for any i ∈ [1,p − 1]. A simple recursion then gives the desired result. When A is not positive semidefinite, we can adapt results fr... |

1286 | Least angle regression - Efron, Hastie, et al. - 2004 |

1195 | Improved approximation algorithms for maximum cut and satisfiability problems using semidefinite programming - Goemans, Williamson - 1995 |

856 | The Dantzig selector: statistical estimation when p is much larger than n - Candès, Tao - 2007 |

544 | Sparse approximate solutions to linear system - NATARAJAN - 1995 |

271 | A Direct Formulation for Sparse PCA Using Semidefinite Programming - d’Aspremont, Ghaoui, et al. |

260 | A branch and bound algorithm for feature subset selection - Narendra, Fukunaga - 1977 |

196 | The Dense k-Subgraph Problem
- Feige, Kortsarz, et al.
- 2001
(Show Context)
Citation Context ...T Az]/β] for some β ≥ 1, we have which means E[z T Az] ≤ q E[zT Az] β q ≤ 1 − + (1 − q) 1T A1 k β − 1 β1 T A1/k E[z T Az] − 1 . 6because 1 T A1/k ≥ E[z T Az]. Now, using Chernoff’s inequality as in (=-=Feige and Seltser, 1997-=-, Lem. 4.1) produces Prob [ Card(z) − 1 T p ≥ t1 T p ] ≤ e − t2 1 T p 3 , so, as in (Feige and Seltser, 1997, Th. 4.1), when k ≥ p1/3 [ Prob Card(z) ≥ k We have 1 T A1 k E[z T Az] ≤ ( 1 + k −1/3)] ≤ e... |

174 | Regression by leaps and bounds - FURNIVAL - 1974 |

129 | Introductory Lectures on Convex Optimization - Nesterov - 2004 |

103 | Learning Multiscale Sparse Representations for Image and Video Restoration,” Multiscale Modeling - Mairal, Sapiro, et al. - 2008 |

64 | Neighborliness of randomly projected simplices in high dimensions - Donoho, Tanner - 2005 |

55 | Approximation algorithms for maximization problems arising in graph partitioning - Feige, Langberg |

52 | On choosing a dense subgraph - Kortsarz, Peleg - 1993 |

11 | A tale of three cousins: Lasso, l2boosting, and danzig - Meinshausen, Rocha, et al. |

10 | Sparse regression as a sparse eigenvalue problem - Moghaddam, Gruber, et al. - 2008 |

9 | Multiscale Modeling and Simulation - SIAM |

2 | and bound in statistical data analysis. The Statistician - Branch - 1981 |