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Dictionary Learning and Tensor Decomposition via the SumofSquares Method
, 2014
"... We give a new approach to the dictionary learning (also known as “sparse coding”) problem of recovering an unknown n × m matrix A (for m> n) from examples of the form y = Ax + e, where x is a random vector in Rm with at most τm nonzero coordinates, and e is a random noise vector in Rn with bounde ..."
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Cited by 2 (0 self)
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there is no guarantee that the local optima of T and T ′ have similar structures. Our algorithm is based on a novel approach to using and analyzing the Sum of Squares semidefinite programming hierarchy (Parrilo 2000, Lasserre 2001), and it can be viewed as an indication of the utility of this very general and powerful
Rounding SumofSquares Relaxations
, 2014
"... We present a general approach to rounding semidefinite programming relaxations obtained by the SumofSquares method (Lasserre hierarchy). Our approach is based on using the connection between these relaxations and the SumofSquares proof system to transform a combining algorithm—an algorithm that ..."
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Cited by 8 (0 self)
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We present a general approach to rounding semidefinite programming relaxations obtained by the SumofSquares method (Lasserre hierarchy). Our approach is based on using the connection between these relaxations and the SumofSquares proof system to transform a combining algorithm—an algorithm
SumofSquares Proofs and the Quest toward Optimal Algorithms
"... Abstract. In order to obtain the bestknown guarantees, algorithms are traditionally tailored to the particular problem we want to solve. Two recent developments, the Unique Games Conjecture (UGC) and the SumofSquares (SOS) method, surprisingly suggest that this tailoring is not necessary and that ..."
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Abstract. In order to obtain the bestknown guarantees, algorithms are traditionally tailored to the particular problem we want to solve. Two recent developments, the Unique Games Conjecture (UGC) and the SumofSquares (SOS) method, surprisingly suggest that this tailoring is not necessary
Quasiconvex SumofSquares Programming
"... Abstract — A sumofsquares program is an optimization problem with polynomial sumofsquares constraints. The constraints and the objective function are affine in the decision variables. This paper introduces a generalized sumofsquares programming problem. This generalization allows one decision ..."
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Abstract — A sumofsquares program is an optimization problem with polynomial sumofsquares constraints. The constraints and the objective function are affine in the decision variables. This paper introduces a generalized sumofsquares programming problem. This generalization allows one
Simplification methods for sumofsquares programs
, 2013
"... Abstract — A sumofsquares is a polynomial that can be expressed as a sum of squares of other polynomials. Determining if a sumofsquares decomposition exists for a given polynomial is equivalent to a linear matrix inequality feasibility problem. The computation required to solve the feasibility ..."
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computation than the convex hull construction. This algorithm is then extended to a more general simplification method for sumofsquares programming. I.
Sumofsquares heuristics for binpacking . . .
, 2001
"... The sumofsquares algorithm (SS) was introduced by Csirik, Johnson, Kenyon, Shor, and Weber for online bin packing of integralsized items into integralsized bins. First, we show the results of experiments from two new variants of the SS algorithm. The first variant, which runs in time O(n √ B log ..."
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The sumofsquares algorithm (SS) was introduced by Csirik, Johnson, Kenyon, Shor, and Weber for online bin packing of integralsized items into integralsized bins. First, we show the results of experiments from two new variants of the SS algorithm. The first variant, which runs in time O(n √ B
Clustering by Maximizing SumofSquared Separation Distance
"... Maximizing the separating margin is crucial for the good generalization performance of Support Vector Machines (SVMs). Analogous to the definition of separation distance or separating margin in SVMs, we propose a definition on separation distance in clustering tasks when a hyperplane is used to sepa ..."
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in the input feature space through an appropriate distance feature mapping. A graphtheoretic perspective of the proposed method is discussed. In particular, we show that, under certain conditions, the proposed clustering algorithm is equivalent to a spectral relaxed graph cut. Extensive experimental results
Noncommutative circuits and the sumofsquares problem
 J. Amer. Math. Soc
"... 1.1. Noncommutative computation. Arithmetic complexity theory studies the computation of formal polynomials over some field or ring. Most of this theory is concerned with the computation of commutative polynomials. The basic model of computation is that of an arithmetic circuit. Despite decades of ..."
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1.1. Noncommutative computation. Arithmetic complexity theory studies the computation of formal polynomials over some field or ring. Most of this theory is concerned with the computation of commutative polynomials. The basic model of computation is that of an arithmetic circuit. Despite decades of work, the best
Hypercontractivity, SumofSquares Proofs, and their Applications
, 2013
"... We study the computational complexity of approximating the 2toq norm of linear operators (defined as ‖A‖2→q = maxv�0‖Av‖q/‖v‖2) for q> 2, as well as connections between this question and issues arising in quantum information theory and the study of Khot’s Unique Games Conjecture (UGC). We show ..."
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close variant of the UGC. We also show that such a good approximation can be computed in exp(n 2/q) time, thus obtaining a different proof of the known subexponential algorithm for SmallSet Expansion. 2. Constant rounds of the “Sum of Squares ” semidefinite programing hierarchy certify an upper bound
Results 1  10
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