17 citations · 60 across the 12 of their papers we have counts for
4 papers · 1 filter
Exponential lower bounds on spectrahedral representations of hyperbolicity cones
Prasad Raghavendra, Nick Ryder, Nikhil Srivastava +1
The Generalized Lax Conjecture asks whether every hyperbolicity cone is a section of a semidefinite cone of sufficiently high dimension. We prove that the space of hyperbolicity co…
The power of sum-of-squares for detecting hidden structures
Samuel B. Hopkins, Pravesh K. Kothari, Aaron Potechin +3
We study planted problems---finding hidden structures in random noisy inputs---through the lens of the sum-of-squares semidefinite programming hierarchy (SoS). This family of power…
Dimension Reduction for Polynomials over Gaussian Space and Applications
Badih Ghazi, Pritish Kamath, Prasad Raghavendra
We introduce a new technique for reducing the dimension of the ambient space of low-degree polynomials in the Gaussian space while preserving their relative correlation structure,…
On the Bit Complexity of Sum-of-Squares Proofs
Prasad Raghavendra, Benjamin Weitz
It has often been claimed in recent papers that one can find a degree d Sum-of-Squares proof if one exists via the Ellipsoid algorithm. In [O17], Ryan O'Donnell notes this widely q…