High Dimensional Regression with Binary Coefficients. Estimating Squared Error and a Phase Transtition

@inproceedings{Gamarnik2017HighDR,
  title={High Dimensional Regression with Binary Coefficients. Estimating Squared Error and a Phase Transtition},
  author={David Gamarnik and Ilias Zadik},
  booktitle={COLT},
  year={2017}
}
1 We consider a sparse linear regression model Y = Xβ∗ +W where X is n× p matrix Gaussian i.i.d. entries, W is n× 1 noise vector with i.i.d. mean zero Gaussian entries and standard deviation σ, and β∗ is p× 1 binary vector with support size (sparsity) k. Using a novel conditional second moment method we obtain a tight up to a multiplicative constant approximation of the optimal squared error minβ ‖Y −Xβ‖2, where the minimization is over all k-sparse binary vectors β. The approximation reveals… CONTINUE READING

From This Paper

Figures and tables from this paper.

References

Publications referenced by this paper.
SHOWING 1-10 OF 17 REFERENCES

Decoding by linear programming , IEEE transactions on information theory 51 ( 2005 ) , no . 12 , 4203 – 4215 . [ Don 06 ] David L Donoho , Compressed sensing

  • Ricardo Restrepo Andrea Montanari, Prasad Tetali
  • Ann . Statist .
  • 2013

, and F . Ricci - Tersenghi , On the solution space geometry of random formulas

  • A. Coja-Oghlan Achlioptas
  • Random Structures and Algorithms
  • 2011

Similar Papers

Loading similar papers…